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GATE CSE 2026 Session 2 Q63: Conditional probability for overlapping sets of coin tosses

Question

Suppose an unbiased coin is tossed 6 times. Each coin toss is independent of all previous coin tosses. Let E1E_1 be the event that among the second, fourth, and sixth coin tosses, there are at least two heads. Let E2E_2 be the event that among the first, second, third, and fifth coin tosses, there are equal number of heads and tails.

The conditional probability P(E1∣E2)P(E_1 \mid E_2) is equal to ____________. (rounded off to one decimal place)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
Show answer and explanation

Answer: 0.5 (official GATE 2026 final answer key)

Concept used: The events share only toss 2; condition on its outcome.

First step: Given E2E_2, toss 2 is a head with probability 1/2 by symmetry; then compute the chance of enough heads among tosses 4 and 6 in each case.

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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