Question - Calculating Probability of Independent Events
Solution:
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 = 1/2Numbers 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 = 1/2Since 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) = 1/4To 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%
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