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

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

by BTGmoderatorDC » Sun Aug 22, 2021 10:23 pm

00:00

A

B

C

D

E

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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

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### Re: A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but no

by swerve » Tue Aug 24, 2021 5:41 am
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

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