Example Question - calculating probability
Here are examples of questions we've helped users solve.
Calculating Probability of Independent Events
To solve this problem, we need to find the probability of two independent events: 1. Landing on a number less than 4. 2. Then landing on a prime number. Let's calculate them one by one: 1. Landing on a number less than 4: The spinner has numbers 1, 2, 3, 4, and 5. The numbers less than 4 are 1, 2, and 3. Hence, there are 3 favorable outcomes out of 5 possible outcomes. So, the probability of landing on a number less than 4 is 3/5. 2. Landing on a prime number: The prime numbers on the spinner are 2, 3, and 5. Therefore, there are 3 prime numbers out of 5 possible outcomes. So, the probability of landing on a prime number is also 3/5. Since both spins are independent events, the combined probability of both events occurring in succession is the product of their individual probabilities: Probability of both events = (Probability of first event) x (Probability of second event) = (3/5) x (3/5) = 9/25 To express this probability as a percentage, we convert the fraction to a decimal and then multiply by 100: 9/25 = 0.36 0.36 x 100 = 36% Therefore, the probability of landing on a number less than 4 and then landing on a prime number is 36%.
Calculating Probability of Independent Events
In this problem, we're trying to find the probability of two independent events occurring in sequence. First, we need to roll a prime number on a 6-sided die, and second, we need to roll a number less than 4. The prime numbers on a 6-sided die are 2, 3, and 5. Since there are 6 possible outcomes when rolling a die, the probability of rolling a prime number is the number of prime outcomes divided by the total number of possible outcomes. There are 3 prime numbers out of 6 possible outcomes, so the probability of rolling a prime number on a 6-sided die is 3/6, which simplifies to 1/2. For the second event, we want to roll a number less than 4. The numbers less than 4 on a 6-sided die are 1, 2, and 3. There are 3 outcomes that satisfy this condition out of 6 possible outcomes, so the probability of rolling a number less than 4 is also 3/6, which simplifies to 1/2. Since these two events are independent (the outcome of the first roll does not affect the outcome of the second), we can find the combined probability by multiplying the probabilities of each event occurring. So, we multiply the probability of rolling a prime number (1/2) by the probability of rolling a number less than 4 (1/2): Combined probability = (1/2) * (1/2) = 1/4 To express this probability as a percentage, we convert the fraction to a decimal and then to a percentage: Decimal form = 1/4 = 0.25 Percentage form = 0.25 * 100 = 25% Therefore, the probability of rolling a prime number and then rolling a number less than 4, in that order, is 25%.
Calculating Probability of Sequential Events
To solve this probability question, we need to calculate the probability of two events happening in sequence: picking a card with the number 1 and then picking an even-numbered card after that without replacing the first card. The first event is picking a 1. There are three cards, and only one of them is a 1, so the probability of picking a 1 is: P(1) = 1/3 Now, if the 1 card has been picked, there are only two cards remaining. To satisfy the second event, we need to pick an even number from the two remaining cards. There is only one even card left (either 2 or 3 was removed, depending on which was picked), so the probability of picking an even number after picking 1 is: P(even | 1) = 1/2 To find the overall probability of both events occurring, we multiply the probabilities of the two events: P(1 and then even) = P(1) * P(even | 1) = (1/3) * (1/2) = 1/6 The probability of picking a 1 and then picking an even number in sequence without replacement is 1/6.
Calculating Probability of Independent Events
The problem is asking for the probability of two independent events: first picking a prime number, and then picking a number greater than 4. To solve this, we'll calculate the probability of each event and then multiply them together because the two events are independent. Prime numbers in the set provided are 2, 3, 5, and 7. There are a total of 8 distinct numbers. So, the probability of picking a prime number is: Number of prime numbers / Total numbers = 4/8 = 1/2 Numbers greater than 4 in the set are 5, 6, 7, and 8. Thus, the probability of then picking a number greater than 4 is again: Number of "greater than 4" numbers / Total numbers = 4/8 = 1/2 Since the events are independent, the overall probability is the product of the two individual probabilities: Probability of prime number AND number greater than 4 = (1/2) * (1/2) = 1/4 To express this as a percentage, we multiply by 100: 1/4 * 100 = 25% Rounded to the nearest tenth of a percent (although in this case there's no need to round since 25% is already at a tenth), the final answer is: 25.0%
Calculating Probability of Independent Events
To solve this problem, we need to calculate the probability of two independent events occurring in sequence: 1. Picking a prime number card. 2. Picking a number greater than 4 card. The sample space consists of 8 cards, numbered from 1 to 8. Among these cards, the prime numbers are 2, 3, 5, and 7. Probability of picking a prime number card = number of prime cards / total number of cards P(prime) = 4/8 = 1/2 After picking a prime number, you replace the card and pick again. The number of cards greater than 4 are 5, 6, 7, and 8. Probability of picking a number greater than 4 = number of cards greater than 4 / total number of cards P(greater than 4) = 4/8 = 1/2 Since these are independent events, we can multiply the probabilities: P(prime and greater than 4) = P(prime) * P(greater than 4) P(prime and greater than 4) = (1/2) * (1/2) P(prime and greater than 4) = 1/4 Converting this into a percentage, we get: P(prime and greater than 4) = (1/4) * 100% = 25% Rounded to the nearest tenth of a percent, the answer remains 25.0%.
Calculating Probability with Divisors and Factors
To solve this problem, we need to determine the divisors of 40 and the factors of 72, then calculate the probability of rolling one of the divisors first, and then calculate the probability of rolling one of the factors afterwards. Given that this appears to involve dice (as indicated by the image of a die), we will assume a standard 6-sided die for our calculations. **Step 1: Divisors of 40** The divisors of 40 are the numbers which divide 40 without leaving a remainder. These are: 1, 2, 4, 5, 8, 10, 20, and 40. However, since we are dealing with a standard die, we are only interested in the divisors that are between 1 and 6 (inclusive), because those are the only outcomes possible with a single roll of the die. The divisors of 40 that fall within this range are: 1, 2, 4, and 5. **Probability of rolling a divisor of 40:** There are 4 favorable outcomes (1, 2, 4, 5) out of 6 possible outcomes (1-6 on a die), so the probability is: P(divisor of 40) = 4/6 = 2/3 after simplifying. **Step 2: Factors of 72** The factors of 72 are the numbers which can be multiplied by another number to get 72. These are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Again, considering we have a standard die, we need the factors that are between 1 and 6. These factors are: 1, 2, 3, 4, and 6. **Probability of rolling a factor of 72:** There are 5 favorable outcomes (1, 2, 3, 4, 6) out of 6 possible outcomes, so the probability is: P(factor of 72) = 5/6. **Step 3: Combined probability** To find the combined probability of both events happening (rolling a divisor of 40 and then a factor of 72), we need to multiply the probabilities of each individual event: P(total) = P(divisor of 40) * P(factor of 72) P(total) = (2/3) * (5/6) Multiplying the fractions, we get: P(total) = (2*5) / (3*6) P(total) = 10 / 18 P(total) = 5 / 9 after simplifying. So, the simplified probability of rolling a divisor of 40 and then rolling a factor of 72 with a standard die is 5/9.
Calculating Probability of Point Location on a Line Segment
The image shows a line segment AB that is divided into sections AC, CD, and DB with lengths 34, 44, and 61 respectively, which sum up to the total length of AB. To find the probability that a random point on AB will be on CD, we can use the following formula: \[ P = \frac{\text{Length of CD}}{\text{Total length of AB}} \] From the image, we know: Length of CD = 44 Total length of AB = 34 (AC) + 44 (CD) + 61 (DB) = 139 Now we can calculate the probability: \[ P = \frac{44}{139} \] To express this as a decimal rounded to the nearest hundredth, calculate 44 divided by 139, which gives approximately: \[ P \approx 0.3165 \] Rounded to the nearest hundredth: \[ P \approx 0.32 \] So, the probability that a random point on AB will be on CD is 0.32, rounded to the nearest hundredth.
Calculating Probability of Coin Flips
To solve this problem, we need to calculate the probability of flipping a coin twice and getting heads on the first flip and tails on the second flip. The probability of getting heads on a single flip is 1/2, and the probability of getting tails on a single flip is also 1/2. Since these two events are independent (the outcome of the first flip does not affect the outcome of the second flip), we can find the combined probability by multiplying the probabilities of the two individual events. So, the probability of getting heads first and then tails is: (1/2) * (1/2) = 1/4. Now to express this as a percentage, we convert the fraction to a percentage by multiplying by 100: 1/4 * 100% = 25%. Therefore, the probability of getting heads and then tails when flipping a coin twice is 25%.
Calculating Probability of Selecting a Good Product
The question is asking for the probability of selecting a good product at random from a total of 10 products, 7 of which are good. The probability (P) of selecting a good product can be calculated using the formula: P(good product) = Number of good products / Total number of products According to the information provided in the question: Number of good products = 7 Total number of products = 10 So the probability is: P(good product) = 7/10 Therefore, the correct answer is D. 7/10.
Calculating Experimental Probability of Drawing a Name
To calculate the experimental probability of drawing Lissa's name from the bowl, you need to divide the number of times Lissa's name was drawn by the total number of draws. From the table provided, you can count the number of times Lissa's name appears. Let's count together: Lissa appears in the following draws: 1, 3, 10, 11, 15. That's 5 times Lissa's name was drawn out of a total of 15 draws. Now, let's calculate the experimental probability: P(Lissa) = Number of times Lissa's name was drawn / Total number of draws P(Lissa) = 5 / 15 To simplify this fraction, you divide both the numerator and the denominator by 5 (their greatest common divisor): P(Lissa) = 1 / 3 Therefore, the experimental probability of drawing Lissa's name is 1/3.
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