The probability that he will be rejected to at least one of the colleges is 0.51.
Given probability that he will admit in A is 0.7, probability that he will not be admit in B is 0.5, probability that atleast one of his applications got rejected is 0.6.
We have to find the probability that he will be rejected to at least one of the colleges.
Probability that he will admit in A =0.7
Probability that he will not admit in A=1-0.7=0.3
Probability that he will not admit in B =0.5
Probability that he will admit in B=1-0.5=0.5
Probability that he will be rejected to at least one of the colleges=probability that he will admit in A* probability that he will not admit in B+ probability that he will admit in B* probability that he will not admit in A+ probability that he will not admit in A* probability that he will not admit in B
=0.7*0.5+0.5*0.3+0.5*0.3
=0.35+0.15+0.15
=0.51
Hence the probability that he will be rejected to at least one of the colleges is 0.51.
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