Question

3 letters are written to 3 persons .3 envelops are taken and names of the persons are written.the letters are inserted into the envelops at random so that each envelop contains 1 letter. find the probability that at least 1 letter is in the correct envelop.

Answer 1

Probability for the correct envelope may be 2/3

Required probability = Number of favorable outcomes /Total number of outcomes

=> n(E)/n(S)

Now,
Let the envelope be denoted by E1, E2, E3 and the corresponding letters by L1, L2, L3

At Least one letter should be in right envelope.

So, let us consider all the favorable outcomes

(i) 1 letter in correct envelope and 2 in wrong envelope.

(i.e) (E1L1, E2L3, E3L2),(E1L3,E2L2,E3L1),(E1L2,E2L1,E3L3)

(ii) Two letter in correct envelope.

(ie) (E1L1,E2L2,E3L3)

∴ No of favorable outcomes = 4

Total no of outcomes =3!=3×2×1=6

∴ Required probability =n(E)/n(S)

⇒4/6

⇒2/3


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