Project ForgeEngineering Mathematics
Calculus
GATE 2020
Hard
A fair coin is tossed 20 times. The probability that 'head' will appear exactly 4 times in the first ten tosses, AND 'tail' will appear exactly 4 times in the next ten tosses is __________ (round off to 3 decimal places).
0.042(± 0.002 accepted)
Explanation
P(exactly 4 heads in first 10) = C(10,4)(0.5)^10 = 210/1024 ≈ 0.20508. By symmetry, P(exactly 4 tails in next 10) is the same, ≈0.20508. Since the two sets of tosses are independent, the joint probability = 0.20508 × 0.20508 ≈ 0.0421.
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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