#### 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?

#### Solution

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) = `1-25/36`

p(4 will come up once) = (36-25)/36=11/36

Is there an error in this question or solution?

Solution Two Dice Are Thrown Simultaneously. What is the Probability That: 4 Will Not Come up Either Time? 4 Will Come up at Least Once? Concept: Probability - A Theoretical Approach.