In a large metropolitan area past records revealed that 30 p

In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college? Please show all your work and dont skip steps

Solution

Since 30% of population go to college, it means that probability of selecting a high school graduate who will go to college = 0.30

no. of graduates = 20, required no. of graduates to go to college = 8

P(graduate will go to college) = 0.30

P(graduate will not go to college) = 1 - 0.30 = 0.70

P( out of 20, exactly 8 will go to college) = ²⁰C₈ * ((0.3)^8) * ((0.7)^12)

= 0.1144

= 0.11 (approximately)