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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 ?

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  • $\begingroup$ 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 $\endgroup$
    – Hussien Mohamed
    Feb 17, 2020 at 9:28

1 Answer 1

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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 $P(A - B)$

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  • $\begingroup$ 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 $\endgroup$
    – Hussien Mohamed
    Feb 17, 2020 at 9:33
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    $\begingroup$ Yes, that's correct. $\endgroup$
    – Adriano
    Feb 17, 2020 at 10:00

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