Chidi and Zainab independently attempt to solve a mathematics problem. The probability tha… — JAMB UTME

Chidi and Zainab independently attempt to solve a mathematics problem. The probability that Chidi solves it is $\frac{3}{5}$ and the probability that Zainab solves it is $\frac{2}{3}$ . What is the probability that exactly one of them solves the problem?

A
$\frac{2}{5}$
B
$\frac{4}{15}$
$\frac{7}{15}$ Cevap
D
$\frac{13}{15}$

Cevap

The probability that exactly one of them solves the problem is

\frac{7}{15}

The correct answer is

\frac{7}{15}

. 'Exactly one' means either Chidi solves the problem while Zainab fails (

P(C \cap Z') = \frac{3}{5} \times \frac{1}{3} = \frac{3}{15}

) OR Zainab solves it while Chidi fails (

P(C' \cap Z) = \frac{2}{5} \times \frac{2}{3} = \frac{4}{15}

). Summing these mutually exclusive probabilities gives

\frac{3}{15} + \frac{4}{15} = \frac{7}{15}

Adım Adım Çözüm

Find the complement probabilities of failure for each student.

Probability Chidi fails,

P(C') = 1 - \frac{3}{5} = \frac{2}{5}

. Probability Zainab fails,

P(Z') = 1 - \frac{2}{3} = \frac{1}{3}

Required to determine individual non-occurrence probabilities.

Calculate the joint probability for each mutually exclusive scenario.

Scenario 1 (Chidi solves, Zainab fails):

\frac{3}{5} \times \frac{1}{3} = \frac{3}{15}

. Scenario 2 (Chidi fails, Zainab solves):

\frac{2}{5} \times \frac{2}{3} = \frac{4}{15}

Since the events are independent, individual probabilities multiply.

Sum the probabilities of the two mutually exclusive outcomes.

Total probability =

\frac{3}{15} + \frac{4}{15} = \frac{7}{15}

By the Addition Law of probability for mutually exclusive compound outcomes.

Anahtar Kavram

Probability of Compound Independent Events

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Adım Adım Çözüm

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