On three consecutive flips of a coin, what is the probability that all three produce the same result?
(A) \(\dfrac1{16}\)
(B) \(\dfrac18\)
(C) \(\dfrac14\)
(D) \(\dfrac38\)
(E) \(\dfrac12\)
Answer: C
Source: Veritas Prep
On three consecutive flips of a coin, what is the probability that all three produce the same result?
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APPROACH #1
P(3 identical flips) = P(1st flip is ANY side AND 2nd flip matches 1st flip AND 3rd flip matches 1st flip)
= P(1st flip is ANY side) x P(2nd flip matches 1st flip) x P(3rd flip matches 1st flip)
= 1 x 1/2 x 1/2
= 1/4
Answer: C
APPROACH #2
P(3 identical flips) = P(3 heads in a row OR 3 tails in a row)
= P(3 heads in a row) + P(3 tails in a row)
= P(1st flip is heads AND 2nd flip is heads AND 3rd flip is heads) + P(1st flip is tails AND 2nd flip is tails AND 3rd flip is tails)
= [P(1st flip is heads) x P(2nd flip is heads) x P(3rd flip is heads)] + [P(1st flip is tails) x P(2nd flip is tails) x P(3rd flip is tails)]
= [1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2]
1/8 + 1/8
= 1/4
Answer: C