On three consecutive flips of a coin, what is the probability that all three produce the same result?

VJesus12 wrote: ↑

Fri Dec 10, 2021 9:07 am

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

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