Question

Two dice are thrown $n$times in succession. Compute

the probability that a double $6$appears at least once. How large need $n$be to make this probability at least$\frac{1}{2}$?

Short answer

Therefore,

$n=25$to make this probability at least$\frac{1}{2}$.

Step-by-step solution

Given Information.

Two dice are thrown $n$times in succession.

Explanation.

$P(double6appearsatleastonce)=1-P(double6neverappears)$

$=1-{(35/36)}^n$

If, $1-(35/36)>\frac{1}{2}$

role="math" localid="1649041592632" $$\begin{gathered} \frac{1}{2}>{(35/36)}^n \\ n>25 \end{gathered}$$