Question

Abstracted secretary placed three letters randomly into three envelopes. What is the probability that at least one of the recipients gets his letter ?

Answer 1

Answer:

The probability is 0.6666

Step-by-step explanation:

First, the total number of ways in which the secretary could place the three letters into three envelopes is calculated using the rule of multiplication as:

    3                *         2               *              1                =     6

1st envelope      2nd envelope     3rd envelope

Because, we have 3 letters for the 1st envelope, then 2 letters for the 2nd envelope and finally 1 letter for the 3rd envelope.

Then, if at least one of the recipients get his letter, it means that:

• All recipients get their letters.
• Just the first recipient receives his letter.
• Just the second recipient receives his letter.
• Just the third recipient receives his letter.

So, we have 4 ways in which at least one of the recipients gets his letter.

Finally, the probability can be calculate as:

$P=\frac{4}{6} = 0.6666$