Q. 2.42 - A First Course in Probability

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$\frac{1}{2}$?

Step-by-Step Solution

Answer

Therefore,

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

Step 1 Given Information.

Two dice are thrown $n$times in succession.

Step 2 Explanation.

$P(double 6 appears at least once)=1-P(double 6 never appears)$

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

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

$$\begin{gathered} \frac{1}{2}>{(35/36)}^n \\ n>25 \end{gathered}$$