Question

I alternately toss a fair coin and toss a fair die until I either toss a head or throw a 2. If I toss the coin first ,the probability that I throw a 2 before I toss a head is

• A. 1/7
• B. 7/12
• C. 5/12
• D. 5/7

Answer 1

The correct option is A

1/7

$P\left(E\right)=P\left(A^{\prime }B\right)+P\left(A^{\prime }{B}^{\prime }{A}^{\prime }B\right)+P\left(A^{\prime }{B}^{\prime }{A}^{\prime }{B}^{\prime }{A}^{\prime }B\right).................$

$P\left(A\right)=$ Probability of getting head $=\frac{1}{2}$

$P\left(B\right)$= Getting a $2=\frac{1}{6}$

This is an infinte GP with common ratio of $P\left(A^{\prime }\right)P\left(B^{\prime }\right)$

$P\left(E\right)=\frac{P\left(A^{\prime }B\right)}{[1-P(A^{\prime }\left)P\right(B^{\prime }\left)\right]}$

$P\left(E\right)=\frac{(\frac{1}{2}\times \frac{1}{6})}{(1-\frac{1}{2}\times \frac{5}{6})}$

$P\left(E\right)=\frac{1}{7}$