A fair coin is tossed 3 times in succession. If the first to
A fair coin is tossed 3 times in succession. If the first toss produced a head, then the probability of getting exactly two heads in 3 tosses ( including the first toss ) is
A1/8
B3/8
C1/2
D3/4
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Answer:\(\frac{3}{4}\)
Explanation:
P(2 heads in 3 tosses / first toss is a head)
(H,H,H)
(H,H,T)
(H,T,H)
(H,T,T)
(T,H,H)
(T,H,T)
(T,T,H)
(T,T,T)
are the 2^3 = 8 ways in which the coin can roll.
Since we are given that the first toss is a head, our sample space becomes:
(H,H,H)
(H,H,T)
(H,T,H)
(H,T,T)
Of these four possibilities, we want to know how many have exactly 2 heads
\(= \frac{3}{4}\)
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