Probability
Probability
nta_abhyas_2025
Grade None
Question:
Fifteen coupons are numbered $1, 2, 3, \ldots, 15$ respectively. Seven coupons are selected at random one at a time with replacement. The probability, that the largest number appearing on selected coupons is at most $B$, is
$\left(\frac{B}{15}\right)^7$ is not here, but $\left(\frac{8}{15}\right)^7$
$\left(\frac{7}{15}\right)^7$ seems not here but $\left(\frac{7}{15}\right)^8$
$\left(\frac{8}{15}\right)^7$
$\left(\frac{7}{15}\right)^8$
Step-by-Step Solution
Key Concept: For independent events, multiply individual probabilities; multiplicative principle applies when selecting with replacement.
Total coupons = 15. We need 1 ≤ selected coupon number ≤ 9, giving coupons numbered 1, 2, 3, 4, 5, 6, 7, 8, 9. Probability of one selected coupon to have number ≤ 9 is $\frac{9}{15} = \frac{3}{5}$. Using the multiplicative principle for independent events, the required probability = $\left(\frac{3}{5}\right) \times \left(\frac{3}{5}\right) \times 7 \text{ times} = \left(\frac{3}{5}\right)^7$.
Correct Answer: 1