Question

Photo and Video Sharing. Photos and videos have become an important part of the online social experience, with more than half of Internet users posting photos or videos online that they have taken themselves. Let A be the event an Internet user posts photos that they have taken themselves, and B be the event an Internet user posts videos that they have taken themselves. Pew Research Center finds that P(A)=0.52,P(b)=0.26,, and P(AorB)=0.54. What is the conditional probability that an Internet user posts photos that they have taken themselves, given that they post videos that they have taken themselves? (Round your answer to three decimal places.)

Answer 1

Answer: 0.923

Explanation:

Let A be the event an Internet user posts photos that they have taken themselves, and B be the event an Internet user posts videos that they have taken themselves.

Pew Research Center finds that

P(A)=0.52 P(b)=0.26, and P(A or B)=0.54.

To find : P(A|B)

Since ,
`\text{P(A or B)=P(A+P(B)-P(A and B)}`

i.e.
`\text{P(A and B)=P(A)+P(B)-P(A or B)}`

`\text{P(A and B)=}0.52+0.26-0.54=0.24`

Now, using conditional probability formula ,

`P(A|B)=\frac{\text{P(A and B)}}{\text{P(B)}}\\\\=(0.24)/(0.26)=0.923076923077\approx0.923`

Hence, the conditional probability that an Internet user posts photos that they have taken themselves, given that they post videos that they have taken themselves = 0.923