Question:
A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4 . Then the conditional probability that the score 4 has appeared atleast once is :
Correct Option: , 4
Solution:
$E_{1}$ [the event for getting score a multiple of 4 ]
$=(1,3),(3,1),(2,2),(2,6),(6,2),(3,5),(5,3),(4,4) \&(6,6)$
$E_{2}[4$ has appeared atleast once $]$
$=(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(4,1),(4,2),(4,3)$,
$(4,5) \&(4,6)$
$E_{1} \cap E_{2}=(4,4)$
$P\left(\frac{E_{2}}{E_{1}}\right)=\frac{1}{9}$
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