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We roll a fair 6-sided die 5 times. What is the probability that we get an odd number in exactly 4 of the 5 rolls?

 Dec 10, 2021
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Since you want one odd number and four even numbers, there are five possibilities:

     OEEEE  +  EOEEE  +  EEOEE  +  EEEOE  +  EEEEO

 

The probability of getting an odd number is 3/6.

The probability of getting an even number is 3/6.

 

Therefore, the probability of OEEEE is  (3/6) x (3/6) X (3/6) x (3/6) x (3/6). = 1/32

This is also the probability of each ot the other possibilities.

 

Adding these together:  (1/32)  +  (1/32)  + (1/32)  +  (1/32)  +  (1/32)  =  5/32

 Dec 10, 2021

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