Q. 144.4( 32 Votes )

(i) the problem is solved (ii) exactly one of them solves the problem.

Answer :

Given:

P(A) = Probability of solving the problem by A = 1/2

P(B) = Probability of solving the problem by B = 1/3

Because A and B both are independent.

⇒ P (A ∩ B) = P(A) . P(B)

⇒ P (A ∩ B) =

P(A^{’}) = 1 – P(A) = 1 – 1/2 = 1/2

P(B^{’}) = 1 – P(B) =

(i) the problem is solved

The problem is solved, i.e. it is either solved by A or it is solved by B.

= P(A ∪ B)

As we know, P (A ∪ B) = P(A) + P(B) - P (A ∩ B)

⇒ P (A ∪ B) =

(ii) exactly one of them solves the problem

i.e. either problem is solved by A but not by B or vice versa

i.e. P(A).P(B^{’}) + P(A^{’}).P(B)

=

=

⇒ P(A).P(B^{’}) + P(A^{’}).P(B) = 1/2

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PREVIOUSTwo balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that(i) both balls are red.(ii) first ball is black and second is red.(iii) one of them is black and other is red.NEXTOne card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?(i) E : ‘the card drawn is a spade’F : ‘the card drawn is an ace’(ii) E : ‘the card drawn is black’F : ‘the card drawn is a king’(iii) E : ‘the card drawn is a king or queen’F : ‘the card drawn is a queen or jack’.

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