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
