When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability

[BTGmoderatorDC]

When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads?

A. 1/4
B. 1/3
C. 5/16
D. 31/64
E. 1/2


OA C

Source: Magoosh

[swerve]

When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads?

A. 1/4
B. 1/3
C. 5/16
D. 31/64
E. 1/2


OA C

Source: Magoosh

Required series is \(HHHTTT = \left(\dfrac{1}{2}\right)^6=\dfrac{1}{64}\)

This combination can occur in \(\dfrac{6!}{3!\ast 3!}\) ways. ie \(20\) ways.

So answer \(=\dfrac{1}{64}\ast 20 = \dfrac{5}{16}\)

Hope this helps!