Two dice are thrown simultaneously. The proba | vedclass

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Question

(C) Let $A$ be the event that the sum is less than $7$ and $B$ be the event that the sum is odd.Total outcomes when two dice are thrown $= 6 	imes 6

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(C) Let $A$ be the event that the sum is less than $7$ and $B$ be the event that the sum is odd.Total outcomes when two dice are thrown $= 6 	imes 6 = 36$.Outcomes for $A$ (sum $$P(A) = \frac{15}{36}$.Outcomes for $B$ (sum is odd): Sums can be $3, 5, 7, 9, 11$. Total $= 18$.$P(B) = \frac{18}{36}$.Outcomes for $A \cap B$ (sum is odd $AND$ less than $7$): Sums can be $3, 5$. Outcomes are $(1,2), (2,1), (1,4), (2,3), (3,2), (4,1)$. Total $= 6$.$P(A \cap B) = \frac{6}{36}$.Using the addition theorem: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.$P(A \cup B) = \frac{15}{36} + \frac{18}{36} - \frac{6}{36} = \frac{27}{36} = \frac{3}{4}$.

Two dice are thrown simultaneously. The probability that the sum is odd or less than $7$ or both is:

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