The coin is flipped 7 times i.e n=7
The probability of getting tails =1/2 on single toss
and probability of getting head=1/2
The total number of possible outcomes is 2^7
[tex]\begin{gathered} =2^7 \\ =128 \end{gathered}[/tex]Total number of possible outcomes=128.
Probability getting 4 tails in total 7 tossed,
Apply combination expression:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]Here we have, n=7, r=4
[tex]\begin{gathered} ^7C_4=\frac{7!}{4!(7-4)!} \\ ^7C_4=\frac{7!}{4!\times3!} \\ ^7C_4=\frac{7\times6\times5\times4!}{4!\times3\times2\times1} \\ ^7C_4=\frac{35}{1} \\ ^7C_4=35 \end{gathered}[/tex]So, the probability of flipping 4 tails out of 7 toss is = 35/128
Percent probabilty=
[tex]\begin{gathered} P=\frac{35}{128}\times100 \\ P=27.34\text{ percent} \end{gathered}[/tex]The probability is 27.34%
