Question

A symmetrical die is thrown 6 times. If getting an odd number is a success, the probability of at the most $5$ successes is

• A. $\frac{5}{64}$
• B. $\frac{15}{64}$
• C. $\frac{63}{64}$
• D. $\frac{36}{64}$

Answer 1

The correct option is C $\frac{63}{64}$

In a die there are $3$ odd numbers: $1,3,5$
Probability of getting an odd number in a single throw of a die is $P=\frac{3}{6}=\frac{1}{2}$
Probability of at the most $5$ successes is$=1-P(X>5)$ ($X$ is number of success)
$=1-P(X=6)$
$=1{-}^6{C}_6(\frac{1}{2}{)}^6=1-\frac{1}{64}=\frac{63}{64}$