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Solution


Q.

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 2nd 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     [2023]
1 A and B are mutually exclusive  
2 The number of favourable cases of the events A, B and C are 15, 6 and 6 respectively.  
3 B and C are independent  
4 The number of favourable cases of the event (A∪B)∩C is 6  

Ans.

(4)

Event A : Number on 1st die < Number on 2nd die

Event B : Number on 1st die = even and number on 2nd die = odd

Event C : Number on 1st die = odd and number on 2nd die = even

n(A)=5+4+3+2+1=15

n(B)=9,   n(C)=9

n((A∪B)∩C)=(A∩C)∪(B∩C)=(3+2+1)+0=6