Question

A bowler knocks down at least $6$ pins $70$ percent of the time.

Out of $200$ rolls, how many times can you predict the bowler will knock down at least $6$ pins?

Answer 1

Compute the value of expectation:

E(knock down at least $6$ pins)$=$number of rolls $\times$probability of knocking down at least $6$ pins.

The total number of rolls is $200$.

It is given that a bowler knocks down at least $6$ pins $70$ percent of the time.

Therefore, the probability to knock down at least $6$ pin is $\frac{70}{100}$.

Substitute $\frac{70}{100}$ for probability of knocking down at least $6$ pins in the equation E(knock down at least $6$ pins)$=$number of rolls $\times$probability of knocking down at least $6$ pins.

E(knock down at least $6$ pins)$=$$200\times \frac{70}{100}$

$\therefore$ E(knock down at least $6$ pins)$=$$140$

Hence, the number of times the bowler will knock down at least $6$ pin is $140$.