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Vilka [71]
3 years ago
12

Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its corre

ct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?A. 1/24B. 1/8C. 1/4D. 1/3E. 3/8
Mathematics
1 answer:
Ad libitum [116K]3 years ago
3 0

Answer:

1/3 is the answer.

Step-by-step explanation:

Tanya prepared 4 different letters to be sent to 4 different addresses.

To solve this we can do the following:

The probability that the 1st letter is in the right envelope is = \frac{1}{4}

The probability that the 2nd letter is in the wrong envelope is = \frac{2}{3}

The probability that the 3rd letter is in the wrong envelope is = \frac{1}{2}

The probability that the 4th letter is in the wrong envelope is = 1

So, the answer becomes: \frac{1}{4}\times \frac{2}{3}\times \frac{1}{2}\times1 = \frac{1}{12}

As we need 4 correct letters in the envelope, we will multiply by 4:

\frac{1}{12}\times4=\frac{1}{3}

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