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Question

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 D P(E1/E2)=1
P(E1)=1P(unit's place in both is 1,2,3,4,6,7,8,9
P(E1=0 or 5)=1(45)2=925
P(E2:5)=P(1 3 5 7 9)P(1 3 7 9)
=14425
=9100
P(E2)P(E1)=9100×254=14
P(E1)=4P(E2)
P(E2/E1)=P(E2E1)P(E1)=P(E2)P(E1)=14
P(E1/E2)=P(E1E2)P(E2)=P(E2)P(E2)=1

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