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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

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by BTGmoderatorDC » Mon May 31, 2021 4:44 pm

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C

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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 Jun 01, 2021 9:59 am
BTGmoderatorDC wrote: ↑
Mon May 31, 2021 4:44 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 try as follows:

Total possible outcomes when coined is tossed \(6\) times \(=2^6=4*4*4=64\)

Total possible outcomes getting \(2\) or \(3\) or \(4\) or \(5\) tails
\begin{align*}
&= 6C2+6C3+6C4+6C5 \\[5pt]
&=\dfrac{6\cdot 5}{2}+\dfrac{6\cdot 5\cdot 4}{3\cdot 2}+\dfrac{6\cdot 5}{2}+6 \\[5pt]
&=15+20+15+6 \\[5pt]
&=56
\end{align*}

Probability of getting at least \(2\) but not more than \(5\) times tails \(=\dfrac{56}{64}=\dfrac{7}{8}\)

Therefore, C
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