Question

Suppose that the population proportion of Internet users who say that they use Twitter or another service to post updates about themselves or to see updates about others is 19%. Think about selecting random samples from a population in which 19% are Twitter users.

Using the notation T for a Twitter user T^c and for a non-Twitter user, if you select three people the sample space is {TTT, TTT^c, TT^cT, T^cTT, TT^cT^c, T^cTT^c, T^cT^cT, T^cT^cT^c}.

Find the following

probabilities:
P(TTT) = _Answer 1_
P(TTT^c) = _Answer 2_
P(TT^cT^c) = _Answer 3_
P(T^cT^cT^c) = _Answer 4_

Give your answers to four decimal places.

Now compute the following to four decimal places.

P(exactly 2 T's) =

P(exactly 1 T) =



Answer 1
Answer 2
Answer 3
Answer 4

Answer 1

We know that

Probability:

​​​​​

Total outcomes=8

Number of TTT in the outcome is 1 hence and total outcome is 8

Answer 1=1/8

=0.1250

Number of TTTc is also 1 hence

Answer 2=1/8

=0.1250

In same way also TTcTc and TcTcTc also is 1 only

Then

Answer 3=1/8

=0.1250

Answer 4=1/8

=0.1250

Exactly 2Ts means that number of T in 3 selection must be 2, not 1 also not 3

We get number of outcomes having 2 number of T=3

Hence P(exactly 2T )=3/8

=0.3750

Also exactly 1T means there should be only 1T in outcome not 2 and not 3

Number of outcomes having exactly 1T =3

P(exactly 1T)=3/8

=0.3750