Question

In paying a bill by mail, you want to put your check and the bill (with a returnaddress printed on it) into a window envelope so that the address shows right sideup and is not blocked by the check. If you put check and bill at random into theenvelope, what is the probability that the address shows correctly?

Short answer

Answer

The probability that the address shows correctly is $\frac{1}{8}$.

Step-by-step solution

Given Information

The check and a bill is to be put inside the envelop such that the address printed on the bill should be visible through the window.

Definition of Independent Event

The events are said to be independent when the occurrence or non-occurrence of any event does not have any effect on the occurrence or non-occurrence of the other event.

When events are independent, apply the formula $P\left(AB\right)=P\left(A\right)·P\left(B\right)$here A and B are the events.

Finding the probability that address is shown correctly

The envelope must contain a cheque and a bill, and each can be positioned in 4 ways, (that is printed side facing the window and opposite and each position having two orientation) and there are two permutations to arrange both.

The number of possible arrangement is $2\times 4\times 4=32$and out of which the ways in where the address is correct is $1\times 1\times 4=4$.

Find the probability that address is shown correctly.

$\frac{4}{32}=\frac{1}{8}$

Thus the required probability is $\frac{1}{8}$.