Question

# A fair die is rolled once, which of the following statement(s) is(are) true?

A
Outcome of an even number is an even chance event.
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B
Outcome of an even number is an unlikely event.
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C
Outcome of a number greater than two is a likely event.
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D
Outcome of a number greater than two is an unlikely event.
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Solution

## The correct option is C Outcome of a number greater than two is a likely event.Let's list the probabilities of different types of events: Given:––––––––– A fair die is rolled once ∴Sample Space={1, 2, 3, 4, 5, 6} ⇒ Total number of possible outcomes =6 Now, let's find the probability of each of the given options one-by-one: As in first option, outcome is an even number, Favorable outcomes ={2, 4, 6} ∴ Number of favorable outcomes =3 Probaility(Even)=Number of favorable outcomesTotal number of possible outcomes Probaility(Even)=36 Probaility(Even)=33×2 Probaility(Even)=12=0.5 As we can see, Probaility(Even)=0.5, outcome of an even number for the given experiment is a even chance event. –––––––––––––––––––––––––––––––––––––––––– In third option, outcome is greater than two, ∴ Favorable outcome ={3, 4, 5, 6} ⇒ Number of favorable outcome =4 Probability{>2}=Number of favorable outcomeTotal number of possible outcomes Probability{>2}=46 Probability{>2}=2×23×2=23 ⇒ 0.5<23<1 ⇒ 0.5<Probability{>2}<1 As we can see, ⇒ 0.5<Probability{>2}<1, outcome of a number greater than two for the given experiment is a likely event.

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