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

Question

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 (A) (2/7) (B) (6/7) (C) (2/9) (D) (4/21)

Tardigrade Admin · Accepted Answer

A: 3 text rd Head occur at 5 text th toss. B: exactly six heads P((A/B))=(P(A ∩ B)/P(B))=( 4 C2 × 4 C2 ×((1/2))9/ 9 C6((1)2)9)=(6.6 ⋅ 6/9 ⋅ 8 ⋅ 7)=(2/7) .

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

$\frac{2}{7}$

$\frac{6}{7}$

$\frac{2}{9}$

$\frac{4}{21}$

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

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

72​

76​

92​

214​