Two numbers are randomly selected and multiplied. Consider two events E1 and E2 defined as E1 : Their product is divisible by 5 E2 : Unit’s places in their product is 5
Which of the following statement is/are correct?
A
E1 is twice as likely to occur as E2
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B
E1 and E2 are disjoint
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C
P(E2/E1)=14
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D
P(E1/E2)=1
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Solution
The correct option is DP(E1/E2)=1 P(E1)=1−P(unit's place in both is1,2,3,4,6,7,8,9 P(E1=0or5)=1−(45)2=925 P(E2:5)=P(13579)−P(1379) =14−425 =9100 P(E2)P(E1)=9100×254=14 P(E1)=4P(E2) P(E2/E1)=P(E2∩E1)P(E1)=P(E2)P(E1)=14 P(E1/E2)=P(E1∩E2)P(E2)=P(E2)P(E2)=1