Question

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

1. 4 will not come up either time?  
2. 4 will come up at least once?

Answer 1

When two dice are thrown, total possible outcomes = 36 

i. 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` 

ii. 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`