Question

A coin tossed three times in succession. if E is the event that there are at least two heads and F is the event in which first throw is a head, then P(E/F) is equal to :

• A. $3/4$
• B. $3/8$
• C. $1/2$
• D. $1/8$

Answer 1

The correct option is A $3/4$

E: event that there are at least 2 heads

F: event in which first throw is head

$P\left(F\right)=\frac{1}{2},P\left(\frac{E}{F}\right)=\frac{P(E\cap F)}{P\left(F\right)}$

For finding $P(E\cap F)$ ,there will be 3 cases

(1) First 2 throws are heads and 3rd is tail

(2) 1st & 3rd throws are heads , 2nd is tail.

(3) All are heads.

So, $P(E\cap F)={\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{2}\right)}^3=\frac{3}{8}$

$P\left(\frac{E}{F}\right)=\frac{\frac{3}{8}}{\frac{1}{2}}=\frac{3}{4}$