Two dice are thrown simultaneously. What is the probability that:… - Vidyadip

Question

Two dice are thrown simultaneously. What is the probability that: 4 will not come up either time? 4 will come up at least once?

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Answer

When two dice are thrown , total possible outccomes=36
Favorable outcomes for 4 will not come up either time:
{(1,1)(1,2)(1,3)(1,5)(1,6)}
{(2,1)(2,2)(2,3)(2,5)(2,6)}
{(3,1)(3,2)(3,3)(3,5)(3,6)}
{(5,1)(5,2)(5,3)(5,5)(5,6)}
{(6,1)(6,2)(6,3)(6,5)(6,6)}
Number of favorable outcomes = 25
p(4 will not come up) = 25/36
P(4 will come up ones) = 1- p(4 will not come up either time)
p(4 will come up once) =$1-\frac{25}{36}$
p(4 will come up once) = (36-25)/36=11/36

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