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Question

A fair coin is flipped once. What is the probability of getting a head and a tail simultaneously? Write the event type.

A
0, Certain event
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B
1, Impossible event
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C
0, Impossible event
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D
1, Certain event
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Solution

The correct option is C 0, Impossible eventFor flipping a fair coin, Sample Space ={H, T} ∴ Total number of outcomes =2 For getting a head and a tail simultaneously, Favorable outcomes ={HT, TH}, which do not belong to the sample space. ∴ Number of favorable outcomes =0 [Favorable outcomes must be taken from sample space only] Hence, the probability of getting a head and a tail simultaneously, P(getting a head and a tail simultaneously)=Number of favorable outcomesTotal number of outcomes=02=0 ∴ Probability of getting both, a head and a tail is 0. That implies the event is impossible. [Events with zero probability are called impossible events] Hence, option (c.) is the correct choice.

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