Question

A recent survey of 2500 college students revealed that during any weekend afternoon, 1364 receive a text message, 857 receive an e-mail and 470 receive both a text message and an e-mail . Suppose a college student is selected at random, what is the probability that he/she neither receives a text message nor an email during any weekend afternoon? Round your answer to four decimal places.

Answer 1

Let's call the event "T" receiving a text message and "E" receiving an e-mail.

From the given information, we can find the number of students who receive either a text message or an e-mail (or both) using the formula for the union of two sets:

Number of students who receive either a text message or an e-mail = Number of students who receive a text message + Number of students who receive an e-mail - Number of students who receive both
= 1364 + 857 - 470
= 1751

The probability of a student neither receiving a text message nor an e-mail is equal to the number of students who don't receive either divided by the total number of students surveyed:

P(neither T nor E) = (2500 - 1751) / 2500
= 749 / 2500
= 0.2996

Rounding to four decimal places:

P(neither T nor E) = 0.2996 ≈ 0.3000