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Question
An unbiased die is thrown once. The probability of getting an even prime number greater than 2 is ______.
Options
`1/2`
`1/3`
`1/6`
0
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Solution
An unbiased die is thrown once. The probability of getting an even prime number greater than 2 is 0.
Explanation:
When a single unbiased die is thrown, the sample space S, which consists of all possible outcomes, is:
S = {1, 2, 3, 4, 5, 6}
The total number of outcomes is n(S) = 6.
2. Determine favorable outcomes
To find the favorable outcomes, we must identify numbers on a die that satisfy two conditions simultaneously:
The number must be an even prime number.
The number must be greater than 2.
The prime numbers on a die are {2, 3, 5}. The only even prime number is 2. Since an even prime number greater than 2 and no such number exists the only even prime is 2 itself, there are no favorable outcomes.
3. Calculate Probability
The number of favorable outcomes is n(E) = 0.
The probability P(E) is calculated as:
`P(E) = "Number of favorable outcomes"/"Total number of outcomes"`
= `0/6`
= 0
