Question

Three letters are dictated to three persons and an envelope is addressed to each
of them, the letters are inserted into the envelopes at random so that each envelope
contains exactly one letter. Find the probability that at least one letter is in its
proper envelope

Answer 1

Three letters are dictated to three persons and an envelope is addressed to each
of them, the letters are inserted into the envelopes at random so that each envelope
contains exactly one letter. Find the probability that at least one letter is in its
proper envelope.

Answer 2

you are asking about the probability of proper letter for three persons or only one person ? means minimum probability or maximum ?

Answer 3

probability that at least one letter is in its
proper envelope

Answer 4

the probability to get a proper letter for each person is 3/9

Answer 5

means 1/3

Answer 6

how

Answer 7

becz there are three letters and the total probability of these letters to deliver is 9

Answer 8

and the probability to get a proper letter for each person is 1/3

Answer 9

1/3 because that is 3/9 in simplest form

Answer 10

get it or not ?

Answer 11

i get it

Answer 12

good

Answer 13

plus its in simplest form

Answer 14

Required probability is given by the number of ways the letters could be placed such that at least one letter is in its correct place divided by the number of ways we could place the letters (favourable ways/total ways).

The total number of ways we could keep them is \(3 \times 2 \times 1 = 6\).

One out of those ways is when all three are in the correct place.
Three other ways when exactly one is in its correct place.

Therefore, the number of favourable cases = 4.

Now we have P = 4/6 = 2/3.

Answer 15

how u got 6

Answer 16

The total number of ways we could kee=6

Answer 17

It makes sense that the probability should be 2/3 rather than 1/3. It's a lot more probable to keep at least one number in the right envelope.