Question

An unbiased die is thrown once. The probability of getting an even prime number greater than 2 is ______.

पर्याय

• `1/2`

• `1/3`

• `1/6`

• 0

Answer 1

An unbiased die is thrown once. The probability of getting an even prime number greater than 2 is 0.

Explanation:

1. Identify total outcomes

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