The probability that an archer hits a target on a given shot

The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer hits the target on three shots out of the five.

The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer doesn’t ever hit the target during the five shots.

The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer hits the target on all five shots

Solution

The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer hits the target on three shots out of the five.

Binomial distribution used.

n=5

p=0.7

P(X=x) = (_nC_x) p^x (1-p)^n-x

P( x=3) =0.3087

The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer doesn’t ever hit the target during the five shots.

P( x=0) =0.0024

The probability that an archer hits a target on a given shot is .7. If five shots are fired, find the probability that the archer hits the target on all five shots

P( x=5) =0.1681

Binomial Probabilities

Data

Sample size

5

Probability of an event of interest

0.7

Statistics

Mean

3.5

Variance

1.0500

Standard deviation

1.0247

Binomial Probabilities Table

X

P(X)

0

0.0024

1

0.0284

2

0.1323

3

0.3087

4

0.3602

5

0.1681