Question

Question 6 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.

Class X1 - Maths -Probability Page 409

Answer 1

Let all three envelopes are denoted by E₁ , E₂ and E₃ and the corresponding letters denoted by L₁ , L₂ and L₃ .

A/C to question,
1 Letter in correct envelope and 2 letters in wrong envelopes may be put as
(E₁L₁ , E₁L₂, E₁L₃ ) , (E₂L₁ , E₂L₂, E₂L₃ ) and (E₃L₁, E₃L₂ , E₃L₃ )

Consequently all three letters are in correct envelope may be put in one way
e.g ( E₁L₁, E₂L₂, E₃L₃ )
Hence, number of favourable cases n ( E ) = 3 + 1 = 4 ways

total number of cases n ( S ) = 3! = 3 × 2 = 6 ways

so, P( E ) = n( E )/n( S ) = 4/6 = 2/3

Answer 2

Answer:

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