Example Question - dice probability
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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.
Probability Distribution of Dice Rolls
a) Theo dữ liệu trong bảng, mặt xúc xắc xuất hiện nhiều nhất là mặt "6 chấm" với 20 lần xuất hiện. b) Tổng số lần gieo là tổng số các lần xuất hiện của tất cả các mặt: 17 (mặt 1 chấm) + 18 (mặt 2 chấm) + 15 (mặt 3 chấm) + 14 (mặt 4 chấm) + 16 (mặt 5 chấm) + 20 (mặt 6 chấm) = 100 lần gieo. c) Xác suất của mỗi mặt xúc xắc được tính bằng số lần mặt đó xuất hiện chia cho tổng số lần gieo. Vậy xác suất của mỗi mặt là: - Mặt 1 chấm: 17/100 = 0.17 hay 17%. - Mặt 2 chấm: 18/100 = 0.18 hay 18%. - Mặt 3 chấm: 15/100 = 0.15 hay 15%. - Mặt 4 chấm: 14/100 = 0.14 hay 14%. - Mặt 5 chấm: 16/100 = 0.16 hay 16%. - Mặt 6 chấm: 20/100 = 0.20 hay 20%. Như vậy, xác suất cao nhất là xác suất xuất hiện của mặt "6 chấm", là 20%.
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