A Die Is Rolled Five Times And The Number Of Fours That Come Up Is Tallied. Find The Probability Of Getting The Given Result. Exactly Three Fours?


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amber Jhon answered
It is a question of binomial distribution and experiment is binomial experiment. In this experiment trials are independent and repeated finite time. The experiment has two possible outcomes which include success and failure. The probability of success remains same throughout the experiment. The formula for binomial distribution is;

P(success)= nCx pxqn-x

p= probability of success

q= probability of failure

n= number of trial

x= possible outcome

In this question P(four)=p= 1/6, q= 5/6 , n=5 and x=3.

P(x=3)= 5C3 (1/6)3 (5/6)5-3

P(x=3)=10* (1/6)3 (5/6)2

P(x=3)= 0.032

The probability of getting four three time when a dice is thrown five time is 0.032

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