Question
Six 6-sided dice are rolled. What is the probability that three of the dice show prime numbers and the rest show composite numbers?
The answer is NOT 5/72
The answer is NOT 5/72
Answers
Scott
probability of prime (1, 2, 3, 5) ... 4/6 = 2/3
... not prime, composite (4, 6) ... 2/6 = 1/3
(p + n)^6 = p^6 + 6 p^5 n + 15 p^4 n^2 + 20 p^3 n^3 + ...
probability 3 prime and 3 not ... 20 * (2/3 * 1/3)^3
... not prime, composite (4, 6) ... 2/6 = 1/3
(p + n)^6 = p^6 + 6 p^5 n + 15 p^4 n^2 + 20 p^3 n^3 + ...
probability 3 prime and 3 not ... 20 * (2/3 * 1/3)^3
mark
answer is 5/54