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5 votes
Find the binomial probability of rolling 5 dice and getting exactly 4 even numbers. 11.6%

15.6%
21.3%
30.9%

User Raphy
by
7.2k points

1 Answer

1 vote
The probability of getting an even number on any one die in a single roll is
\frac12.

For 5 dice, the probability of rolling
x even numbers (where
0\le x\le5) is


p(x)=\dbinom5x\left(\frac12\right)^x\left(1-\frac12\right)^(5-x)

p(x)=\dbinom5x\left(\frac12\right)^5


You then have


p(4)=\dbinom54\left(\frac12\right)^5=(5!)/(2^54!(5-4)!)=\frac5{2^5}\approx0.156=15.6\%
User Nitin Garg
by
7.5k points