Question

Three coins are tossed simultaneously. Let E be the event of getting at most two heads and F be the event of getting only two heads. Are the events E and F mutually exclusive? Justify your answer.
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Answer 1

Answer:

First, we need to find P(E),P(F),P(G),P(E⋂F),P(F⋂G),P(E⋂G)

Total combinations are:HHH,HHT,HTH,THH,HTT,THT,TTH,TTT→8

From this combinations, we can directly say that,

P(E)=

8

2

P(F)=

8

4

P(G)=

8

7

P(E⋂F)= only one possibility that is all are head=

8

1

P(F⋂G)= exactly two heads=

8

3

P(E⋂G)= only one possibility that is all are tail=

8

1

Now we can multiply and equate and then check which are equal, so we get

(A) as answer.

Hence, (A) is correct.

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