Question

Chances that three persons A, B, and C go to the market are 30%, 60% and 50% respectively. The probability that at least one will go to the market is :

• A. $\frac{14}{10}$
• B. $\frac{43}{50}$
• C. $\frac{9}{100}$
• D. $\frac{7}{50}$

Hint:

To find the probability of at least one event occurring, calculate the complement of the probability of none of the events happening.

Answer 1

The Correct Option is B

The probability that at least one of the persons will go to the market is the complement of the probability that none of them goes to the market.
- Probability that person A does not go to the market: $P(A') = 1 - 0.30 = 0.70$
- Probability that person B does not go to the market: $P(B') = 1 - 0.60 = 0.40$
- Probability that person C does not go to the market: $P(C') = 1 - 0.50 = 0.50$
The probability that none of them goes to the market is: \[ P(A' \cap B' \cap C') = P(A') \times P(B') \times P(C') = 0.70 \times 0.40 \times 0.50 = 0.14 \] Now, the probability that at least one will go to the market is: \[ P(\text{at least one}) = 1 - P(A' \cap B' \cap C') = 1 - 0.14 = 0.86 \] Thus, the probability that at least one will go to the market is $\frac{43}{50}$.