When two dice are thrown simultaneously,what | vedclass

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(B) The total number of possible outcomes when two dice are thrown is $6^2 = 36$.Let $E$ be the event that at least one die shows a number greater tha

Vedclass · Accepted Answer

$3/4$

Vedclass · Answer

(B) The total number of possible outcomes when two dice are thrown is $6^2 = 36$.Let $E$ be the event that at least one die shows a number greater than $3$.It is easier to find the probability of the complement event $E'$,where neither die shows a number greater than $3$.This means both dice must show a number from the set $\{1, 2, 3\}$.The number of outcomes for $E'$ is $3 	imes 3 = 9$.The outcomes are: $(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)$.Therefore,$P(E') = \frac{9}{36} = \frac{1}{4}$.The probability of the required event is $P(E) = 1 - P(E') = 1 - \frac{1}{4} = \frac{3}{4}$.

When two dice are thrown simultaneously,what is the probability that at least one of the dice shows a number greater than $3$?

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