180% of the people at a dating site are single, and 20% are married. A single pe

Question

180% of the people at a dating site are single, and 20% are married. A single person tells the truth about marital status 95% of the time. A married person tells the truth 50% of the time. Given that a person claiming to be single is telling the truth?

2A soccer goalie is expected to stop 10 out of her next 100 penalty kicks. Assuming each kick is an independent event with identical probability of being stopped, what is the standard deviation of the number of kicks she will stop out of the next 100?

3A survey asks people which political party they favor most strongly. Is the result a cardinal, nominal or ordinal variable?

Explanation / Answer

Question 1:

Here we are given that:

P( single ) = 0.8, P( married ) = 0.2,

Here we are also given that: P( says single | single ) = 0.95

Then we have here: P( says married | married ) = 0.5

Using law of total probability, we get:

P( says single ) = P( says single | single )P( single ) + P( says single | married )P( married )

P( says single ) = 0.95*0.8 + 0.5*0.2 = 0.86

Here, we have to compute P( single | says single ) using bayes theorem as:

P( single | says single ) = P( says single | single )P( single ) / P( says single )

P( single | says single ) = 0.95*0.8 / 0.86

P( single | says single ) = 0.8837

Therefore 0.8837 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.