# A fair coin is tossed $3$ times. Find the probability of (a) throwing $3$ heads, given that the first toss is a head. [closed]

A fair coin is tossed $3$ times. Find the probability of :-

(a) throwing $3$ heads, given that the first toss is a head.

(b) throwing $3$ heads, given that the first two tosses result in heads.

## closed as off-topic by Dragonemperor42, Davide Giraudo, Chris Godsil, C. Falcon, LeucippusApr 24 '17 at 3:18

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• What have you tried? Hint: If your first toss is a head, then your sample space is of the form $H,_,_$ ; where _ can be either H or T. – Dragonemperor42 Apr 23 '17 at 17:21
• @elizabeth-han i tried to use condtional formula but my answer is 1/8 and the answer of book is 1/4 – user373141 Apr 23 '17 at 17:24
• @prayersmith I assume you're talking about part A. What's the conditional formula and how did you apply it? – Elizabeth Han Apr 23 '17 at 17:28

(a) Note that if $A$ designates event that you throw 3 heads and $B$ designates event that your first throw is head, then $A\cap B$ =$A$, because $B\subseteq A$
So $P(A\cap B)=P(A)=(1/2)^3$
$P(B)=1/2\cdot1\cdot1$
Now $P(A|B)=\frac{P(A\cap B)}{P(B)}=1/4$