Question

Two dice are rolled. A = ‘sum of two dice equals 4’ B = ‘sum of two dice equals 3’ C = ‘at least one of the dice shows a 2’

What is P(B)?

What is P(A|C)?

What is P(B|C)?

Answer 1

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

A= {(1,3), (2,2), (3,1)}

B={(1,2), (2,1)}

C={(1,2)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,2)(4,2)(5,2)(6,2)}

AnC = {(2,2)}

BnC={(1,2), (2,1)}

P(B) = n(B)/n(S) = 2/36 = 1/18

P(A|C) = n(AnC)/n(C) = 1/11

P(B|C) = n(BnC)/n(C) = 2/11