Respuesta :
Answer:
The required probability is [tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex].
Step-by-step explanation:
Consider the provided information.
A committee of 9 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis,
The probability of yea or nay vote is equal, = [tex]\frac{1}{2}[/tex]
So, we can say that [tex]p=q=\frac{1}{2}[/tex]
Use the formula: [tex]P(x)=\binom{n}{x}p^xq^{n-x}[/tex]
Where n is the total number of trials, x is the number of successes, p is the probability of getting a success and q is the probability of failure.
We want proposal wins by a vote of 7 to 2, that means the value of x is 7.
Substitute the respective values in the above formula.
[tex]P(x)=\binom{9}{7}(\frac{1}{2})^7(\frac{1}{2})^{9-7}[/tex]
[tex]P(x)=\frac{9!}{7!2!}(\frac{1}{2})^7(\frac{1}{2})^{2}[/tex]
[tex]P(x)=\frac{8\times9}{2}\times(\frac{1}{2})^9[/tex]
[tex]P(x)=\frac{4\times9}{2^9}[/tex]
[tex]P(x)=\frac{9}{2^7}[/tex]
[tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex]
Hence, the required probability is [tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex].
