# The probability of missing the target

On a firing range, a rifleman has two attempts to hit a target. The probability of hitting the target with the first shot is $$0.2$$ and the probability of hitting with the second shot is $$0.3$$. The probability of hitting the target with both shots is $$0.1$$

Find the probability of:

a) missing the target with both shots

b) hitting with the first shot and missing with the second

My turn :

1):

The probability of missing the first shot is $$0.8$$ and the probability of missing the second shot $$0.7$$

Then

The probability of missing the two shots is $$0.8 \times 0.7 = 0.56$$

2):

The probability of hitting the first and missing the second is $$0.2 \times 0.7 = 0.14$$

Are these solutions correct ?

• There is an information in the question says that the probability of hitting the target in the two shots is $0.1$ but is we calculated it from the given it will be $0.2 \times 0.3 = 0.6$ what is wrong ? @Florian Ingels – Hussien Mohamed Feb 17 '20 at 9:28

## 1 Answer

No, the two events are not independent, so you can't just multiply probabilities.

Hint: Draw a Venn diagram. Given $$P(A)$$, $$P(B)$$, and $$P(A \cap B)$$, we're asked to find $$1 - P(A \cup B)$$ and $$P(A - B)$$

• Thank you , i have tried it as you told me , i got the first is $0.6$ and the second is $0.1$ Is it true ? @Adriano – Hussien Mohamed Feb 17 '20 at 9:33
• Yes, that's correct. – Adriano Feb 17 '20 at 10:00