JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Probability

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A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is p, then 96p is equal to ____.

Answer: 9

Solution

The first six and last five tosses overlap in positions

4, 5, 6

; let

k

be the number of heads there. Then positions

1

3

carry

4 - k

heads and positions

7

8

carry

3 - k

heads, which requires

k \in {1, 2, 3}

. The number of favourable sequences is

k = 1 \sum 3 (k 3) (4 - k 3) (3 - k 2) = (1 3) (3 3) (2 2) + (2 3) (2 3) (1 2) + (3 3) (1 3) (0 2) = 3 + 18 + 3 = 24

. With

2^{8} = 256

equally likely outcomes,

p = \frac{24}{256}

, so

96 p = 96 \cdot \frac{24}{256} = 9

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Integer answer

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