Question

1.      A telephone survey uses a random digit dialing machine to call subjects. The random digit dialing machine is expected to reach a live person 15% of the time.

a.      True or False: Each call is an independent random event.

In two attempts, what is the probability of achieving......

b.      exactly two successful calls? (success = reach a live person)

c.      one success and one failure (in any order)?

Im having trouble with part (c). Are they looking for the Pr of one success and one failure? Or do I have to average out the two probabilities? The "in any order" is confusing me

Answer 1

A telephone survey uses a random digit dialing machine to call subjects . The random digit dialing machine is expected to reach a live person 15% of the time

Therefore probability of success is p=0.15

Here each call is an independent random event as random dialing machine dialing digit randomly each time .

So this is true sentence

A) True.

Now in two attempts

So n=2

This is binomial distribution with n=2, p=0.15

b) probability of exactly 2 success is,

P(x=2)=

P(x=2)= 0.0225

C) Probability of one success and one failure means probability of exactly one success,

P(x=1)=

P(x=1)=0.255.

Probability of one success and one failure(in any order) is 0.255

For c) other way

Probability of one success and ons failure is

= First success and second failure + first failure and second success

= 0.15*0.85+0.85*0.15

=0.1275+0.1275

=0.255