Question

-) 2000 students are surveyed regarding their choices of courses. 550 of them said that they will pick math next semester. 680 of them said that they will pick statistics and 750 students said that they will choose Economics next semester. Considering that a student cannot take these courses in the same semester a) What is the probability that we pick a student at random who is going to take math next term? b) What is the probability that we randomly choose a student who is going to take both math and economics next semester? c) What is the probability that we randomly choose a student who is not going to choose economics next semester?

Answer 1

Answer:

1.

P(Understudies who take Math) = 550 / 2000

= 0.275

P(Understudies who take Statistics) = 680 / 2000

= 0.34

P(Understudies who take Economics) = 750 / 2000

= 0.375

P(Understudies who don't take any courses) = 20 / 2000

= 0.01

a)

P(Understudies who take Math) = 550 / 2000

= 0.275

b)

P(Understudies who is going to take both Math and Economics ) = P ( understudies who take Math)*P(Understudies who take Economics )

substitute values

= 0.275*0.375

= 0.1031

c)

P(Understudies who won't take Economics ) = 1 - P (Understudies who take Economics)

substitute values

= 1 - 0.375

= 0.625

2.

sample n = 8

p = 0.94

Binomial distribution P(X) = nCr*p^r*q^(n-r)

nCr = n!/(n-r)!*r!

a)

P(X = 8) = 8C8*0.94^8*(1-0.94)^0

= 0.6096

b)

P(X >= 1) = 1 - P(X < 1)

= 1 - P(0)

= 1 - 8C0*0.94^0*(1-94)^8

= 1 - 0.00000000017

= 0.999999999

= 1