Question:medium

What is the probability of getting seventh head in the tenth toss of an unbiased coin?

Show Hint

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
  • \(21/256\)
  • \(15/128\)
  • \(21/128\)
  • \(15/256\)
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Consider all \(2^{10}=1024\) equally likely sequences of 10 coin tosses.
Step 2: We want sequences where toss 10 is Heads and exactly 6 of the first 9 tosses are Heads, so that the 7th Head lands exactly on toss 10.
Step 3: The number of such sequences equals the number of ways to place 6 heads among the first 9 positions, with the 10th position fixed as Head: $$\binom{9}{6} = 84$$
Step 4: So the probability is $$\frac{84}{1024} = \frac{21}{256}$$
\[\boxed{\frac{21}{256}}\]
Was this answer helpful?
0