JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Probability

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From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :-

(A) $\frac{7}{1 0 ^{7}}$
(B) $\frac{81}{1 0 ^{8}}$
(C) $\frac{67}{1 0 ^{8}}$
(D) $\frac{73}{1 0 ^{8}}$ ✓ Correct

Answer: (D)

Solution

With replacement, each draw is defective with probability

p = \frac{1}{10}

and non-defective with

q = \frac{9}{10}

. For at least

7

defective out of

8

P (7) = (7 8) (\frac{1}{10})^{7} (\frac{9}{10}) = \frac{72}{1 0 ^{8}}

and

P (8) = (\frac{1}{10})^{8} = \frac{1}{1 0 ^{8}}

. Adding, the probability is

\frac{73}{1 0 ^{8}}

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Single correct option

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