Question

A die is thrown twice. What is the probability that

(i) $5$ will not come up either time? (ii) $5$ will come up at least once?

Answer 1

Throwing a die twice and throwing two dice simultaneously are treated as the same experiment.

Sample space $=\left\{\right(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)$

$(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)$

$(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)$

$(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)$

$(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)$

$(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$

i) $P(5$ will not come up either time$)=$ Number of times $5$ does not show divided by total number of outcomes

$P(5$ will not come up either time$)=\frac{25}{36}$

ii) $P(5$ will come up at least once$)=$ Number of times $5$ shows up at least once divided by total number of outcomes

$P(5$ will come up at least once$)=\frac{11}{36}$