JEE Advanced (True/False): Probability

Q. 1. If the letters of the word "Assassin" are written down at random in a row, the probability that no two S's occur together is 1/35 (1983 - 1 Mark)

Ans. Sol. Let E be the event "No two S's occur together".
A, A, I, N can be arranged in    ways

- A - A - I - N - Creating 5 places for 4 S. Out of 5 places 4 can be selected in ⁵ C₄ = 5 ways.

\ No two S's occur together in = 12 × 5 = 60 ways Total no.of arranging all letters of word 'assassin'

\ Req. prob.  =  \ Statement is False.

Q.2. If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is 0.5. (1989 - 1 Mark)

Ans. Sol.  P (A ∪  B) = P (A) + P (B) - P (A ∩ B)
= P (A) + P (B) - P (A) P (B)
[∵A and B are independent events] = 0.2 + 0.3 - 0.2 × 0.3 = 0.5 - 0.06 = 0.44 ≠ 0.5
\ The statement is false.