Respuesta :
Answer:
The probability of getting 2 or fewer women when 10 people are picked
P(x≤ 2) = [tex]\frac{56}{1024} = 0.0546[/tex]
Step-by-step explanation:
The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women
That is probability of participants of television quiz of equal numbers of men and women that is 50 %of men and 50% of women.
p = 50/100 = 1/2
q = 1-p = 1 - 1/2 = 1/2
n =10
we will use binomial distribution [tex]p(x =r) = n_{cr} p^{r} q^{n-r}[/tex]
The probability of getting 2 or fewer women when 10 people are picked
P(x≤ 2) = P(x=0)+P(x=1)+P(x=2)
= [tex]10_{c0} \frac{1}{2} ^{0} (\frac{1}{2}) ^{10-0}+ 10_{c1} \frac{1}{2} ^{1} (\frac{1}{2}) ^{10-1 \\[/tex] + [tex]10_{c2} \frac{1}{2} ^{2} (\frac{1}{2}) ^{10-2[/tex]
by using formula [tex]n_{cr} =\frac{n!}{(n-r)!r!}[/tex]
on simplification we get
= [tex]10_{c0} (\frac{1}{2}) ^{10}+ 10_{c1} (\frac{1}{2}) ^{10)[/tex] + [tex]10_{c2} (\frac{1}{2}) ^{10)[/tex]
= [tex]1 (\frac{1}{2}) ^{10}+ 10(\frac{1}{2}) ^{10)[/tex]+[tex]45 (\frac{1}{2}) ^{10}[/tex]
= [tex]\frac{56}{1024} = 0.0546[/tex]
Conclusion:-
The probability of getting 2 or fewer women when 10 people are picked
P(x≤ 2) = [tex]\frac{56}{1024} = 0.0546[/tex]
