You pick a card at random. Without putting the first card back, you pick a second card at random.6789What is the probability of picking a prime number and then picking a prime number?Write your answer as a percentage rounded to the nearest tenth.
Question
You pick a card at random. Without putting the first card back, you pick a second card at random.6789What is the probability of picking a prime number and then picking a prime number?Write your answer as a percentage rounded to the nearest tenth.
Solution
Sure, let's break this down:
First, we need to know how many prime numbers are in a deck of cards. The prime numbers under 10 are 2, 3, 5, and 7. Since there are four suits in a deck, there are 4*4 = 16 prime number cards in a deck of 52 cards.
The probability of drawing a prime number on the first draw is therefore 16/52 = 0.3077.
Since we're not replacing the first card, there are now 51 cards left in the deck, and only 15 prime number cards left.
So, the probability of drawing a prime number on the second draw is 15/51 = 0.2941.
The probability of both events happening is the product of their individual probabilities, so the probability of drawing a prime number twice in a row is 0.3077 * 0.2941 = 0.0904.
Converting this to a percentage and rounding to the nearest tenth gives us 9.0%.
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