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Most Important Selected Qs for JEE AdvancedMathematicsProbability

A man has 3 coins A, B and C, A is unbiased, the probability that a head will result when B is tossed is 2 3 , the probability that a head will result when C is tossed is 1 3 . One of the coin chosen at random and is tossed 3 times, giving a total of two heads and one tail. ( array ll Column-I & Column-II (A) The probability that the chosen coin was A & (p) 32 75 (B) The probability that the chosen coin was B & (q) 1

Options

  1. A( A ) ( q ) ;( B ) ( t ) ;( C ) ( p ) ;( D ) ( s )
  2. B( A ) ( p ) ;( B ) ( s ) ;( C ) ( q ) ;( D ) ( t )
  3. C( A ) ( s ) ;( B ) ( p ) ;( C ) ( q ) ;( D ) ( q )
  4. D( A ) ( t ) ;( B ) ( q ) ;( C ) ( p ) ;( D ) ( s )

Correct answer

C. ( A ) ( s ) ;( B ) ( p ) ;( C ) ( q ) ;( D ) ( q )

Step-by-step solution

Let E be the event of getting 2 head and I tail aligned & P(A)=P(B)=P(C)= 1 3 & P(E / A)= ^3 C₂ ( 1 3 )^2= 3 8 P(E / B)= ^3 C₂ ( 2 3 )^2 ( 1 3 )= 4 9 & P(E / C)= ^3 C₂ ( 1 3 )^2 ( 2 3 )= 2 9 aligned So by Baye's theorem P ( A / E )= 9 25 , P ( B / E )= 32 75

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