Example Question - spinner
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Probability of Landing on Specific Numbers on a Spinner
To solve this problem, we need to consider the two steps described: first landing on a number less than 4, and then landing on a prime number. From the image of the spinner, we can see that there are 5 sections, each containing the numbers from 1 to 5. Let's work on the first part: The probability of landing on a number less than 4. Numbers less than 4 on the spinner are 1, 2, and 3. That means there are 3 favorable outcomes out of the 5 possible outcomes. So, the probability P(less than 4) is 3/5 or 60%. Now, for the second part: The probability of landing on a prime number after we have already landed on a number less than 4. The prime numbers on the spinner are 2, 3, and 5. However, the second spin is independent of the first, meaning that we consider the probability of landing on a prime number out of all possible outcomes again - which are 2, 3, and 5 again. So, there are again 3 favorable outcomes out of the 5 possible outcomes. The probability P(prime number) is therefore also 3/5 or 60%. The overall probability of both events happening in sequence (landing on a number less than 4 and then landing on a prime number) is the product of their individual probabilities: P(less than 4) * P(prime number) = (3/5) * (3/5) = 9/25. To express this as a percentage, we compute: (9/25) * 100% = 36%. Therefore, the probability of landing on a number less than 4 and then on a prime number, when spinning this spinner twice, is 36%.
Probability of Landing on a Factor of 16 and Even Number
To solve this problem, let's look at the two events: 1. Landing on a factor of 16 2. Landing on an even number Considering the first event, the factors of 16 are 1, 2, 4, 8, and 16. From the spinner, we want to find the numbers that are factors of 16. The spinner contains the numbers 1, 2, 4, 6, 7, 8, and 9. The factors of 16 present on the spinner are 1, 2, 4, and 8. There are 4 favorable outcomes out of 7 possible outcomes, so the probability of the first event is 4/7. For the second event, we need to find the probability of landing on an even number. The even numbers on the spinner are 2, 4, 6, and 8. There are 4 even numbers out of 7 possible outcomes, so the probability of the second event is also 4/7. Now, these two events are independent because the result of the first spin does not affect the result of the second spin. Therefore, the combined probability of both events occurring is the product of their individual probabilities: Probability of landing on a factor of 16 and then an even number = (Probability of landing on a factor of 16) * (Probability of landing on an even number) = (4/7) * (4/7) = 16/49 Therefore, the probability of landing on a factor of 16 and then landing on an even number when spinning the spinner twice is 16/49.
Calculating Probability of Landing on Factor of 16 and Even Number
To find the probability of landing on a factor of 16 and then landing on an even number after spinning the spinner twice, let's break down the problem into two separate events: 1. Landing on a factor of 16. 2. Landing on an even number. For the first event, we'll identify the factors of 16 from the numbers available on the spinner. The positive factors of 16 are 1, 2, 4, 8, and 16. Now, let's see which of these are present on the spinner. I can see the numbers 8 and 4 on the spinner, both of which are factors of 16. For the second event, we'll identify which numbers are even. The even numbers on the spinner are 4, 6, and 8. Now we calculate the probability for each event and then multiply them to find the total probability of both events happening in sequence (assuming the spinner is fair and each number has an equal chance of being landed on). 1. Probability of landing on a factor of 16: There are two factors of 16 on the spinner (4 and 8) out of 8 possible numbers. So the probability is 2/8 or simplified to 1/4. 2. Probability of landing on an even number regardless of the first spin: There are three even numbers on the spinner (4, 6, and 8) out of 8 possible numbers. So the probability is 3/8. Multiplying the two probabilities together gives the final probability: (1/4) * (3/8) = 3/32 So, the probability of landing on a factor of 16 and then landing on an even number is 3/32.
Probability Problem Involving Spinner
I can see that the image contains a question about a probability problem involving a spinner. The problem states that the spinner is divided into equally sized sections, 3 of which are gray and 5 of which are blue. The question asks for the probability that the first spin lands on gray and the second spin lands on blue. To solve this, we need to calculate the probability of both events happening one after the other. The chance that the first spin lands on gray is 3 out of 8, as there are 3 gray sections out of a total of 8. The probability of a specific event is calculated by the formula: \[ P(\text{Event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \] For the first spin: \[ P(\text{first spin on gray}) = \frac{3}{8} \] For the second spin, the probability that the spin lands on blue is 5 out of 8, as there are 5 blue sections. For the second spin: \[ P(\text{second spin on blue}) = \frac{5}{8} \] Since these are independent events, the overall probability of both occurring in sequence is the product of the two individual probabilities: \[ P(\text{gray then blue}) = P(\text{first spin on gray}) \times P(\text{second spin on blue}) \] \[ P(\text{gray then blue}) = \left( \frac{3}{8} \right) \times \left( \frac{5}{8} \right) \] \[ P(\text{gray then blue}) = \frac{3 \times 5}{8 \times 8} \] \[ P(\text{gray then blue}) = \frac{15}{64} \] So, the probability that the first spin lands on gray and the second spin lands on blue is \(\frac{15}{64}\).
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