(a) An unbiased die is thrown once. Find the probability of getting (i) a number greater than 3 (ii) an even prime number. OR (b) A box contains 5 red, 8 white and 4 green marbles. One marble is drawn from the box at random. Find the probability of (i) getting a white marble (ii) not getting a green marble.

Step 1: Identify Sample Space and Events for Part (a)

When an unbiased die is thrown once, the possible outcomes are the numbers from 1 to 6. This set of all possible outcomes is called the sample space, denoted by $S$. The total number of outcomes is 6.

Step 2: Calculate Probability for Part (a)(i)

For part (a)(i), we need to find the probability of getting a number greater than 3. The numbers in the sample space that are greater than 3 are 4, 5, and 6. There are 3 such outcomes. The probability is the number of favorable outcomes divided by the total number of outcomes.

Step 3: Calculate Probability for Part (a)(ii)

For part (a)(ii), we need to find the probability of getting an even prime number. The only even prime number is 2. There is only 1 such outcome. The probability is the number of favorable outcomes divided by the total number of outcomes.

Step 4: Identify Total Marbles and Events for Part (b)

For part (b), we have a box containing 5 red, 8 white, and 4 green marbles. The total number of marbles in the box is the sum of the marbles of each color, which is 17. This is our total number of outcomes.

Step 5: Calculate Probability for Part (b)(i)

For part (b)(i), we need to find the probability of getting a white marble. There are 8 white marbles. The probability is the number of white marbles divided by the total number of marbles.

Step 6: Calculate Probability for Part (b)(ii)

For part (b)(ii), we need to find the probability of not getting a green marble. We can calculate this by subtracting the probability of getting a green marble from 1. There are 4 green marbles, so the probability of getting a green marble is 4/17. Alternatively, the number of non-green marbles is $5 \text{ (red)} + 8 \text{ (white)} = 13$. So the probability is $13/17$.

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