probablity

Number Theory Level 2

A is known to hit targets in 2 of 5 shots. B is known to hit in 3 of 4 shots. Find the probablity of the target being hit when both try.

2 solutions

Vibha Sharma
Nov 13, 2015

P(hit) = 1 - P(no hit)

P(no hit) = when both try but none hit

P(A hit) = 2/5

P(A not hit) = 3/5

P(B hit) = 3/4

P(B not hit) = 1/4

P(hit) = 1 - (2/5)(1/4)

        = 17/20 

        =0.85

Tom Engelsman
Dec 16, 2020

We are interested in the probability of the target being hit by either $A$ or $B$ . This can be expressed according to:

$P(A \cup B) = P(A) + P(B) - P(A\cap B) = \frac{2}{5} + \frac{3}{4} - (\frac{2}{5})(\frac{3}{4}) = \boxed{\frac{17}{20}}.$