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Engineering Mathematics
Probability & Statistics
GATE 2010
Hard

X and Y are independent random variables. X follows a binomial distribution, with N=5 and p=1/2. Y takes integer values 1 and 2, with equal probability. Then the probability that X=Y is

  • 15/64
  • B15/32
  • C1/2
  • D15/16

Explanation

P(X=Y)=P(X=1)P(Y=1)+P(X=2)P(Y=2). P(X=1)=C(5,1)(0.5)⁵=5/32. P(X=2)=C(5,2)(0.5)⁵=10/32. P(X=Y)=0.5×(5/32)+0.5×(10/32)=7.5/32=15/64.

Source: GATE CH 2010 (2010)

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