A recent poll conducted by the Globe and Mail indicated that

A recent poll conducted by the Globe and Mail indicated that 7 percent of Canadians felt effect from the recent CBC lockout. Two Canadians are randomly polled. Using four decimals in your answers, what is the probability that
(a) both will indicate they have felt no effect from the recent CBC lockout? Equation Editor

(b) at least one will indicate they have felt no effect from the recent CBC lockout? Equation Editor

(c) If at least one indicated they have felt no effect from the recent CBC lockout, what is the probability that both have felt no effect from the recent CBC lockout? Equation Editor

(d) If five Canadians are to be randomly polled, what is the probability that at least one is effected by the CBC lockout?

Solution

p=0.07 [felt effect ] ; n=2;

a) prob that both will have no effect = (1-p)^2 = 0.93^2 =0.8649

b) prob that at least one will felt no effect = prob that 1 will felt no effect + prob that 2 will felt no effect

     =(1-p)^2 + 2C1 (1-p)p = (1-p)[1-p+2p] = (1-p^2) = 0.9951

c) P(X=2/X=1,2) = P(X=2 and X=1,2)/ P(X=1,2) = P(X=2)/P(x=1,2) = 0.8649/0.9951 =0.8692

d) n=5;

Prob that at least 1 wil be affected = 1- Prob that no one will be affected = 1- (1-p)^5 =0.3043