Question - Probability Calculation for Sequential Events
Solution:
To solve this problem, we need to find the probability of two independent events occurring one after the other: picking a prime number and then picking a number greater than 4.There are 8 cards in total.Prime numbers in the set are 2, 3, 5, and 7. There are four prime numbers.Numbers greater than 4 in the set are 5, 6, 7, and 8. There are four numbers greater than 4.Since the events are independent (picking one card does not influence the next one, because the card is put back), we can multiply the probabilities of each event to get the total probability.The probability of picking a prime number is 4 out of 8 (since there are 4 prime numbers out of 8 total numbers). That gives us:P(prime) = 4/8 = 1/2The probability of picking a number greater than 4 is also 4 out of 8 (since there are 4 numbers greater than 4 out of 8 total numbers). That gives us:P(greater than 4) = 4/8 = 1/2Now, we multiply these probabilities together:P(prime and greater than 4) = P(prime) × P(greater than 4)P(prime and greater than 4) = 1/2 × 1/2P(prime and greater than 4) = 1/4As a percentage, we can calculate this by multiplying by 100:P(prime and greater than 4) = 1/4 × 100 = 25%So, the probability of picking a prime number and then picking a number greater than 4 is 25%. Since the question asks to round to the nearest tenth, our final answer remains 25.0%.
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