Two marksmen, Kemi and Chidi, independently shoot at a target once. The probability that K… — JAMB UTME

Two marksmen, Kemi and Chidi, independently shoot at a target once. The probability that Kemi hits the target is $0.7$ , and the probability that Chidi hits the target is $0.6$ . What is the probability that at least one of them hits the target?

Cevap: 0.88

Cevap

The probability that at least one marksman hits the target is 0.88.

Since the two shooting attempts are independent, the probability that both marksmen miss is

(1 - 0.7) \times (1 - 0.6) = 0.3 \times 0.4 = 0.12

. Subtracting this probability from 1 yields

1 - 0.12 = 0.88

, which represents the probability that at least one marksman hits the target.

Adım Adım Çözüm

Find the probability of each event not occurring (missing the target).

P(\text{Kemi misses}) = 0.3

and

P(\text{Chidi misses}) = 0.4

The sum of an event's probability and its complement is always 1.

Determine the probability of both events failing simultaneously.

P(\text{both miss}) = 0.3 \times 0.4 = 0.12

For independent events

A

and

B

P(A' \cap B') = P(A') \times P(B')

Use the complement rule to find the probability of at least one success.

P(\text{at least one hits}) = 1 - 0.12 = 0.88

The event 'at least one hits' is the exact complement of 'neither hits'.

Anahtar Kavram

Compound probability laws for independent events and complement of combined events

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