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14 votes
14 votes
Nine cards are numbered from 1 to 9 and placed in a box. One card is selected at random and not replaced. Another card is randomly selected. What is the probability of selecting two prime numbers?

User Robin Hawkes
by
2.4k points

2 Answers

19 votes
19 votes

Answer:

1/6

Explanation:

There are 4 possible primes: 2, 3, 5, 7

First card has 4/9 probability of being a prime. Second card has 3/8 probability of being a prime(since 3 prime cards left and 8 total cards left because we do not replace the first card). 4/9 * 3/8 = 1/6.

Another way to do this is using combinatorics. C(9,2) = 36 ways to choose 2 distinct cards, C(4,2) = 6 ways to choose two of the "prime" cards. 6/36 = 1/6.

User Usul
by
3.1k points
20 votes
20 votes

Answer:

1/6

Explanation:

There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.

User Scott Bellware
by
3.1k points