Problem Solving

A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

A. 5/8
B. 3/4
C. 7/8
D. 57/64
E. 15/16


OA C

Source: Princeton Review

BTGmoderatorDC wrote: ↑

Sun Aug 22, 2021 10:23 pm

A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

A. 5/8
B. 3/4
C. 7/8
D. 57/64
E. 15/16


OA C

Source: Princeton Review

Let's find it out the other way:

P of all head(or no tail)\(=\dfrac{1}{2^6}=\dfrac{1}{64}\)

P of all tail (or no head)\(=\dfrac{1}{2^6}=\dfrac{1}{64}\)

P of one tail\(=\dfrac{1}{2^6} \ast 6\) ( multiply by 6 as there are 6 ways we can get one tail and each is having a probability of \(1/2\))

Total\(=\dfrac{1}{64} + \dfrac{1}{64} + \dfrac{6}{64}=\dfrac{1}{8}\)

Reqd P\(=1-\text{Total}=1-\dfrac{1}{8}=\dfrac{7}{8} \Longrightarrow\) C