Question

10.   Smartphone usage among people fifty-five (55) years and older has increased

                over the last several years. It is now reported that 35% (.35) of people over the age of

                55 own a smartphone. Ten (10) persons 55 or over were asked at a local mall if they

                owned a smartphone. What is the probability that:

                           a. No more than two (2) people owned a smartphone?

                           b. Exactly one (1) person owned a smartphone?

                           c. Less than three (3) people owned a smartphone?

                           d. At least two (2) people owned a smartphone?

                           e. Two (2) or three (3) people owned a smartphone?

                           f. What is the probability that if ten persons were asked if they owned a

                              smartphone on two consecutive days that exactly one person owned a

                              smartphone.

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other.

Here we need to use the binomial formula.

P(r) = ncr*(p^r)*(1-p)^n-r

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

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.35

N = number of trials = 10

R = desired success

A)

P(0) + P(1) + P(2)

= 0.26160739138

B)

P(1) = 10c1*(0.35^1)*(1-0.35)^10-1

= 0.07249169493

C)

P(0) + p(1) + P(2) {less than 3}

= 0.26160739138

D)

P(at least 2) = 1 - (p(0) + p(1))

= 0.91404556173