GATE EC 2016 Set 3 — Question 13
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Question
The probability of getting a “head” in a single toss of a biased coin is . The coin is tossed repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting "head" for the first time in the fifth toss is
Correct answer
0.07 to 0.08
Solution
Let
Let
We want to find the probability of getting a "head" for the first time in the fifth toss.
This means the first four tosses must be tails, and the fifth toss must be a head.
Since the tosses are independent, the probability is:
P(H) be the probability of getting a head in a single toss, so .Let
P(T) be the probability of getting a tail in a single toss, so .We want to find the probability of getting a "head" for the first time in the fifth toss.
This means the first four tosses must be tails, and the fifth toss must be a head.
Since the tosses are independent, the probability is:
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