In an electrical power station, two independent backup transformers, T_1 and T_2, operate … — JAMB UTME

In an electrical power station, two independent backup transformers, $T_1$ and $T_2$ , operate simultaneously during power surges. The probability that $T_1$ fails during a surge is $0.15$ , and the probability that $T_2$ fails during the same surge is $0.20$ . What is the probability that at least one transformer functions correctly during a power surge?

Cevap: 0.97

Cevap

0.97

The failure probabilities are

P(F_1) = 0.15

and

P(F_2) = 0.20

. By the multiplication law for independent events, the probability of both failing is

P(F_1 \cap F_2) = 0.15 \times 0.20 = 0.03

. Using the complement rule, the probability of at least one functioning correctly is

1 - P(F_1 \cap F_2) = 1 - 0.03 = 0.97

Adım Adım Çözüm

Determine the joint probability of both transformers failing.

P(F_1 \cap F_2) = 0.15 \times 0.20 = 0.03

Since the operational failures of the two transformers are independent events, the probability of both failing together is the product of their individual failure probabilities.

Calculate the probability that at least one transformer functions correctly.

P(\text{at least one functions}) = 1 - 0.03 = 0.97

The event that at least one transformer functions is the complement of the event that both transformers fail simultaneously.

Anahtar Kavram

Independent Compound Events and the Complement Rule

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