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CBSE Class 12-science Answered

A die is thrown twice and the sum of the numbers appearing is observed to be 8 . what is the conditional probability that the number 5 has appeared at least once.
Asked by haroonrashidgkp | 04 Nov, 2018, 08:27: PM
answered-by-expert Expert Answer
Consider x be the number on the first die and y be the number on the second die.
According to the question,
we need to find
P(x + y = 8/ x = 5 or y = 5) 
begin mathsize 16px style straight P left parenthesis straight x plus straight y equals 8 divided by straight x equals 5 space or space straight y equals 5 right parenthesis equals fraction numerator straight P left parenthesis straight x plus straight y equals 8 space ans space straight x equals 5 space or space straight y equals 5 right parenthesis over denominator straight P left parenthesis straight x equals 5 space or space straight y equals 5 right parenthesis end fraction Possible space outcomes space for space straight x plus straight y equals 8 space and space straight x equals 5 space or space straight y equals 5 space are space left curly bracket left parenthesis 3 comma 5 right parenthesis comma left parenthesis 5 comma 3 right parenthesis right curly bracket Hence comma straight P left parenthesis straight x plus straight y equals 8 space ans space straight x equals 5 space or space straight y equals 5 right parenthesis equals 2 over 36 Possible space outcomes space for space straight x equals 5 space or space straight y equals 5 space are space left curly bracket left parenthesis 1 comma 5 right parenthesis comma left parenthesis 2 comma 5 right parenthesis comma left parenthesis 3 comma 5 right parenthesis comma left parenthesis 4 comma 5 right parenthesis comma left parenthesis 5 comma 5 right parenthesis comma left parenthesis 6 comma 5 right parenthesis comma left parenthesis 5 comma 1 right parenthesis comma left parenthesis 5 comma 2 right parenthesis comma left parenthesis 5 comma 3 right parenthesis comma left parenthesis 5 comma 4 right parenthesis comma left parenthesis 5 comma 6 right parenthesis right curly bracket Hence comma straight P left parenthesis straight x equals 5 space or space straight y equals 5 right parenthesis equals 11 over 36 Required space probability equals fraction numerator begin display style 2 over 36 end style over denominator begin display style 11 over 36 end style end fraction equals 2 over 11 end style
Answered by Sneha shidid | 08 Nov, 2018, 11:07: AM

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