The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. among the last 10 participants there have been only 2 women. if participants are picked randomly, what is the probability of getting 2 or fewer women when 10 people are picked

The probability of getting 2 or fewer women when 10 people are picked

P(x≤ 2) =

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

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)

          =   +

          by using formula

on simplification we get

     = +

    = +

  =

Conclusion:-

The probability of getting 2 or fewer women when 10 people are picked

P(x≤ 2) =

30 people weigh 160 pounds or more