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  4. If a fair coin is tossed 9 times then probability that 3 text rd head occurs on 5 text th toss, given that exactly 6 head occurred, is

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Q. If a fair coin is tossed 9 times then probability that $3^{\text {rd }}$ head occurs on $5^{\text {th }}$ toss, given that exactly 6 head occurred, is

Probability - Part 2

Solution:

$A: 3^{\text {rd }}$ Head occur at $5^{\text {th }}$ toss.
$B$ : exactly six heads
$P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}=\frac{{ }^4 C_2 \times{ }^4 C_2 \times\left(\frac{1}{2}\right)^9}{{ }^9 C_6\left(\frac{1}{2}\right)^9}=\frac{6.6 \cdot 6}{9 \cdot 8 \cdot 7}=\frac{2}{7} .$