Two marksmen fire at a target simultaneously. Jiri hits the target 70% of the time and Benita hits the target 80% of the time. How do you determine the probability that Jiri hits it but Benita misses?

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Answer 1 · 2016-07-05T20:57:12

Probability is 0.14.

Disclaimer: It's been a long time since I have done stats, I hopefully shook the rust off here but hopefully someone will give me a double check.

Probability of Benita missing $= 1 -$ $= 1 -$ Probability of Benita hitting.

$P_{B m i s s} = 1 - 0.8 = 0.2$ $P_(Bmiss) = 1 - 0.8 = 0.2$

$P_{J h i t} = 0.7$ $P_(Jhit) = 0.7$

We want the intersection of these events.

As these events are independent we use the multiplication rule:

$P_{B m i s s} ⋂ P_{J h i t} = P_{B m i s s} \cdot P_{J h i t} = 0.2 \cdot 0.7 = 0.14$ $P_(Bmiss) nnn P_(Jhit) = P_(Bmiss)*P_(Jhit) = 0.2*0.7 = 0.14$