Question

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result.

More than three twos.

A.

0.433

B.

0.564

C.

0.905

D.

0.403

Answer 1

Probability (P) (k successes out of n trials) = nCk * p^k * (1-p)^(n-k), where nCk = n! / (k! * (n-k)!)

for this problem n=20, p = 1/6(probability of rolling 1 two) is approximately 0.1667

P ( of getting more that 3 two's) = 1 -P(0 two's out of 20 trials) -P(1 two out of 20 trials) -P(2 two's out of 20 trials) -P(3 two's out of 20 trials)

P ( of getting more that 3 two's) = 1 -0.026 -0.104 -0.198 -0.238 = 0.434

My answer is A