Two dices are tossed. The probability that the total score is a prime number is

Sure, let's solve this step by step.

Step 1: Identify the total number of outcomes When two dice are thrown, the total number of outcomes is 6*6 = 36 because a die has 6 faces.

Step 2: Identify the favorable outcomes The prime numbers between 2 and 12 (the minimum and maximum possible scores) are 2, 3, 5, 7, and 11. We need to find the number of ways to get these scores.

• For 2: There's only one way to get this (1,1). So, 1 favorable outcome.
• For 3: There are two ways to get this (1,2) and (2,1). So, 2 favorable outcomes.
• For 5: There are four ways to get this (1,4), (4,1), (2,3), and (3,2). So, 4 favorable outcomes.
• For 7: There are six ways to get this (1,6), (6,1), (2,5), (5,2), (3,4), and (4,3). So, 6 favorable outcomes.
• For 11: There are two ways to get this (5,6) and (6,5). So, 2 favorable outcomes.

So, the total number of favorable outcomes is 1+2+4+6+2 = 15.

Step 3: Calculate the probability The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So, the probability that the total score is a prime number is 15/36 = 5/12.