Question

The probability that an amateur golfer actually hits the ball is 1/10. If four separate attempts are made, find the probability that the ball will be hit.
a) four time
b) at least twice
c) not at all​

Answer 1

not at all because
10=1
20=2
30=3
40=4

Answer 2

Given: Probability that an amateur golfer hits the ball is 1/10. 4 attempts are made.

To find: Probability that ball was hit:

1- 4 times

2- at least twice

3- not at all

Explanation: This is a question of Bernoulli's theorem. Here probably of success(p)= 1/10 and probability of failure (q)= 1-1/10= 9/10

First case: Ball was hit 4 times-

P(4 times) =

$1 - \binom{4}{0} {p}^{0} {q}^{4}$

$1 - \binom{4}{0} { \frac{1}{10} }^{0} { \frac{9}{10} }^{4}$

= 3439/10000

Second case: Ball was hit at least twice=

$1 - \binom{4}{0} { \frac{1}{10} }^{0} { \frac{9}{10} }^{4} - \binom{4}{1} { \frac{1}{10} }^{1} { \frac{9}{10} }^{3}$

= 523/10000

Third case: Not at all

$\binom{4}{0} { \frac{1}{10} }^{0} { \frac{9}{10} }^{4}$

= 6561/10000

Therefore, the probability to hit the ball all times, at least twice and not at all are 3439/10000, 523/10000 and 6561/10000 respectively.