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  • Two dice are thrown independently. Let A be the event that the number appeared on the 1st die is less than the number appeared on the 2nd die, B be the event that the number appeared on the 1st die

Two dice are thrown independently. Let A be the event that the number appeared on the 1st die is less than the number appeared on the 2nd die, B be the event that the number appeared on the 1st die is even and that on the second die is odd, and C be the event that the number appeared on the 1st die is odd and that on the 2nd is even. Then :

Option: 1

the number of favourable cases of the events A, B and C are 15,6 and 6 respectively


Option: 2

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


Option: 3

B and C are independent


Option: 4

A and B are mutually exclusive


Answers (1)

best_answer

\begin{aligned} & A=\{(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)(3,4),(3,5),(3,6)(4,5),(4,6),(5,6)\} \\ & n(A)=15 \end{aligned}

\begin{aligned} & B=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\} \\ & n(B)=9 \\ & C=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\} \\ & n(C)=9 \\ & ((A \cup B) \cap C)=\{(1,2),(1,4),(1,6),(3,4),(3,6),(5,6)\} \\ & \Rightarrow n((A \cup B) \cap C)=6 \end{aligned}

Posted by

Devendra Khairwa

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