2 unbiased dice are thrown. Find the probabil | vedclass

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(A) Let $A$ be the event of getting a doublet and $B$ be the event of getting a total of $10$.The sample space $S$ has $6 	imes 6 = 36$ outcomes.The

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$\frac{7}{9}$

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(A) Let $A$ be the event of getting a doublet and $B$ be the event of getting a total of $10$.The sample space $S$ has $6 	imes 6 = 36$ outcomes.The set of doublets is $A = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\}$,so $n(A) = 6$.The set of outcomes with a total of $10$ is $B = \{(4,6), (5,5), (6,4)\}$,so $n(B) = 3$.The intersection $A \cap B = \{(5,5)\}$,so $n(A \cap B) = 1$.The probability of $A \cup B$ is given by $P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{6}{36} + \frac{3}{36} - \frac{1}{36} = \frac{8}{36} = \frac{2}{9}$.The probability that neither a doublet nor a total of $10$ appears is $1 - P(A \cup B) = 1 - \frac{2}{9} = \frac{7}{9}$.

$2$ unbiased dice are thrown. Find the probability that neither a doublet nor a total of $10$ will appear.

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