Two dice are thrown independently. Let A be t | vedclass

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Question

(A) Let the outcomes of the two dice be $(x, y)$ where $x, y \in \{1, 2, 3, 4, 5, 6\}$. The total number of outcomes is $6 	imes 6 = 36$.Event $A$: $

Vedclass · Accepted Answer

the number of favourable cases of the event $(A \cup B) \cap C$ is $6$

Vedclass · Answer

(A) Let the outcomes of the two dice be $(x, y)$ where $x, y \in \{1, 2, 3, 4, 5, 6\}$. The total number of outcomes is $6 	imes 6 = 36$.Event $A$: $x Event $B$: $x \in \{2, 4, 6\}$ and $y \in \{1, 3, 5\}$. The number of outcomes is $3 	imes 3 = 9$.Event $C$: $x \in \{1, 3, 5\}$ and $y \in \{2, 4, 6\}$. The number of outcomes is $3 	imes 3 = 9$.Now,$(A \cup B) \cap C = (A \cap C) \cup (B \cap C)$.$B \cap C$: $x$ is even and odd,which is impossible,so $B \cap C = \emptyset$.$A \cap C$: $x If $x=1$,$y \in \{2, 4, 6\}$ ($3$ cases).If $x=3$,$y \in \{4, 6\}$ ($2$ cases).If $x=5$,$y \in \{6\}$ ($1$ case).Total cases for $A \cap C = 3 + 2 + 1 = 6$.Thus,the number of favourable cases for $(A \cup B) \cap C$ is $6 + 0 = 6$.

Similar Questions

$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is:

The probability of getting the number $5$ when throwing a fair die is:

When two dice are thrown simultaneously,find the probability of the following:
$(1)$ The numbers are the same.
$(2)$ The difference between the numbers is $1$.

The probability of obtaining an even prime number on each die,when a pair of dice is rolled,is . . . . . . .

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