Question:
What is the probability of getting seventh head in the tenth toss of an unbiased coin?
What is the probability of getting seventh head in the tenth toss of an unbiased coin?
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The 7th head lands on toss 10 only if exactly 6 heads occur in the first 9 tosses and toss 10 is itself a head, use the negative binomial pmf.
Updated On: Jul 4, 2026
- \(21/256\)
- \(15/128\)
- \(21/128\)
- \(15/256\)
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The Correct Option is A
Solution and Explanation
Step 1: The 7th head occurring exactly on the 10th toss means among the first 9 tosses there are exactly 6 heads (and 3 tails), and the 10th toss itself is a head.
Step 2: Probability of exactly 6 heads in 9 tosses: \[\binom{9}{6}\left(\frac{1}{2}\right)^9 = \frac{84}{512}\]
Step 3: Multiply by the probability that the 10th toss is a head, \(1/2\): \[\frac{84}{512}\times\frac{1}{2} = \frac{84}{1024} = \frac{21}{256}\]
The required probability is \(21/256\).
Step 2: Probability of exactly 6 heads in 9 tosses: \[\binom{9}{6}\left(\frac{1}{2}\right)^9 = \frac{84}{512}\]
Step 3: Multiply by the probability that the 10th toss is a head, \(1/2\): \[\frac{84}{512}\times\frac{1}{2} = \frac{84}{1024} = \frac{21}{256}\]
The required probability is \(21/256\).
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