In a simultaneous throw of a pair of dice, find the probability of getting (a) a doublet. (b) a sum greater than 9. Explain with diagram and images or figure if possible in the video and write all step by step solution of each question in simplest way for class 8 child

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Welcome! Today we'll solve a probability problem involving two dice. When we throw a pair of dice simultaneously, we want to find the probability of getting a doublet and the probability of getting a sum greater than 9. Let's start by understanding that each die has 6 faces, so the total number of possible outcomes when throwing two dice is 6 times 6, which equals 36. Let's look at the complete sample space. When we throw two dice, we can represent each outcome as an ordered pair. The first number represents what we get on the first die, and the second number represents what we get on the second die. Here we can see all 36 possible outcomes arranged in a grid. Each row represents the outcomes when the first die shows a particular number, and each column represents different values of the second die. Now let's solve part A: finding the probability of getting a doublet. A doublet means both dice show the same number. Looking at our sample space, the doublets are: one-one, two-two, three-three, four-four, five-five, and six-six. That's 6 favorable outcomes out of 36 total outcomes. So the probability equals 6 divided by 36, which simplifies to 1 over 6. Now let's solve part B: finding the probability of getting a sum greater than 9. This means we need sums of 10, 11, or 12. For sum equals 10, we have: four-six, five-five, and six-four. For sum equals 11, we have: five-six and six-five. For sum equals 12, we have: six-six. That's 6 favorable outcomes out of 36 total outcomes. So the probability is 6 over 36, which also simplifies to 1 over 6. Let's summarize our solutions. For part A, the probability of getting a doublet is 1 over 6. For part B, the probability of getting a sum greater than 9 is also 1 over 6. Both answers are the same, which is just a coincidence! Remember, probability is always calculated as the number of favorable outcomes divided by the total number of possible outcomes. In both cases, we had 6 favorable outcomes out of 36 total outcomes, giving us the same probability of 1 over 6.