A fair die is cast 4 times. Calculate the probability of obtaining exactly two 6's.?

Question

Round to the nearest tenth of the percentage

Answer 1

This is binomial distribution (Bernoulli trials), with probability of success (sixes) p = 1/6 &  probability of failure 5/6.

 

The term representing P(2 successes, 2 failures) is equal to ₄C₂ times (1/6)² and also times (5/6)² = 0.11574.

 

I believe that Richard's calculation is not correct (omits factor (5/6) squared).

Answer 2

Hi Lizette,

 

Getting two 6's in four rolls can happen in 6 ways. ₄C₂ = 6 The probability of getting two 6's is 1/36. Therefore, 6 times 1/36 = 1/6 or .16666666... Converting to a percent to the nearest 10th is 16.7%