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An unbiased die thrown twice. Let the ev...

An unbiased die thrown twice. Let the event A be 'even number on the first throw' and B the event 'even no. on the second throw'. Check the independence of the events A and B.

Text Solution

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If all the 36 elementary events of the experiment are considered to be equally likely, we have
`P(A) = 18/36=1/2 " and " P(B)=18/36=1/2`
Also, `P(AcapB)`= P(even no. of both throws)
`=9/36=1/4`
Now, `P(A).P(B)=1/2xx1/2=1/4`
Clearly, `P(AcapB)=P(A)xxP(B)`
Thus, A and B are independent events.
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