Question

If the probability is 0.70 that any one person interviewed at a shopping mall will be against an increase in the sales tax to finance a new football stadium,

(a) What is the probability that among four persons interviewed at the mall the first three will be against the increase in the sales tax, but the fourth will not be against it?

(b) What is the probability that among four persons interviewed at the mall three will be against the increase in the sales tax?

(c) What is the probability that among ten persons interviewed at the mall seven will be against the increase in the sales tax?

(d) What is the probability that the fourth person interviewed is the first to be against the increase in the sales tax?

(e) What is the probability that seven persons will be interviewed before ending four who will be against the increase in the sales tax?

Answer 1

Given data:

probability that any one person interviewed at a shopping mall will be against an increase in the sales tax to finance a new football stadium, p= 0.70

probability that any one person interviewed at a shopping mall will be not against an increase in the sales tax to finance a new football stadium,q=1- p= 1-0.70 = 0.30

(a)

the probability that among four persons interviewed at the mall the first three will be against the increase in the sales tax, but the fourth will not be against it = P(a) = p*p*p*q =0.7*0.7*0.7*0.3

P(a) =0.1029

The probability that among four persons interviewed at the mall the first three will be against the increase in the sales tax, but the fourth will not be against it is 0.1029

(b)

the probability that among four persons interviewed at the mall three will be against the increase in the sales tax =P(b)

n=4

r=3

p(b)=0.4116

The probability that among four persons interviewed at the mall three will be against the increase in the sales tax is 0.4116

(c)

the probability that among ten persons interviewed at the mall seven will be against the increase in the sales tax =p(c)

n=10

r=7

p(c)=0.26683

The probability that among ten persons interviewed at the mall seven will be against the increase in the sales tax is 0.26683

(d)

the probability that the fourth person interviewed is the first to be against the increase in the sales tax,=p(d)

p(d) = fisrt 3 not agaist & 4th is against

p(d) = q*q*q*p

p(d) = 0.3*0.3*0.3*0.7

p(d) =0.0189

The probability that the fourth person interviewed is the first to be against the increase in the sales tax is 0.0189

(e)

The probability that seven persons will be interviewed before ending four who will be against the increase in the sales tax= p(e)

n=7

r=4

p(e)=0.22689

The probability that seven persons will be interviewed before ending four who will be against the increase in the sales tax is 0.22689