In an archery competition, two archers, Kemi and Chidi, attempt to hit a target independen… — JAMB UTME

In an archery competition, two archers, Kemi and Chidi, attempt to hit a target independently. The probability that Kemi hits the target is $\frac{1}{3}$ and the probability that Chidi hits the target is $\frac{2}{5}$ . What is the probability that at least one of them hits the target?

$\frac{3}{5}$ Cevap
B
$\frac{11}{15}$
C
$\frac{2}{15}$
D
$\frac{13}{15}$

Cevap

The probability that at least one archer hits the target is

\frac{3}{5}

For independent events, the probability of both events occurring is

P(K \cap C) = P(K) \times P(C) = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15}

. Applying the addition law of probability

P(K \cup C) = P(K) + P(C) - P(K \cap C)

gives

\frac{1}{3} + \frac{2}{5} - \frac{2}{15} = \frac{9}{15} = \frac{3}{5}

Adım Adım Çözüm

Identify event probabilities and independence

P(\text{Kemi}) = \frac{1}{3}

and

P(\text{Chidi}) = \frac{2}{5}

The problem specifies that the two attempts are independent events.

Calculate the joint probability (intersection) using the multiplication law for independent events

P(\text{Kemi} \cap \text{Chidi}) = P(\text{Kemi}) \times P(\text{Chidi}) = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15}

For independent events, the probability of both occurring together is the product of their individual probabilities.

Apply the addition law of probability to find the union

P(\text{Kemi} \cup \text{Chidi}) = \frac{1}{3} + \frac{2}{5} - \frac{2}{15} = \frac{5 + 6 - 2}{15} = \frac{9}{15} = \frac{3}{5}

The addition law states

P(A \cup B) = P(A) + P(B) - P(A \cap B)

to prevent double counting the intersection.

Anahtar Kavram

Compound Events, Multiplication Law for Independent Events, and Addition Law of Probability

Tahmini Süre:1m 30s

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