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John and Mary are taking a mathematics course. The course [#permalink]
04 Nov 2003, 14:01
John and Mary are taking a mathematics course. The course has only three grades: A, B, and C. The probability that John gets a B is .3. The probability that Mary gets a B is .4. The probability that neither gets an A but at least one gets a B is .1. What is the probability that at least one gets a B but neither gets a C?
P (Desired event ) = Neither gets C but atleast one gets B
Let us define the following
Ja = probability that John gets A
Jb = probability that John gets B
Jc = probability that John gets C
Ma = probability that Mary gets A
Mb = probability that Mary gets B
Mc = probability that Mary gets C
Desired event = Ma Jb + Mb Jb + Mb Ja
We also know that Ma+Mb+Mc = 1 and Ja+Jb+Jc = 1
Ma = 1- ( Mb + Mc ) and Ja = 1 - ( Jb + Jc )