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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.

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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%.

This problem has been solved

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