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 But image u showed of two dice is not correct.one has 6 dots and other has 4 dots in starting part of video explanation..pls show correct images of dice for showing total outcomes 36.. carefully
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Welcome! Today we'll solve probability problems with two dice. When we throw two dice together, each die can show any number from 1 to 6. Since there are 6 possibilities for the first die and 6 possibilities for the second die, the total number of possible outcomes is 6 times 6, which equals 36.
Here are all 36 possible outcomes when we throw two dice. The first number in each pair represents the result of the first die, and the second number represents the result of the second die. For example, (1,1) means both dice show 1, (1,2) means the first die shows 1 and the second die shows 2, and so on. This complete list helps us calculate probabilities for any event.
Now let's solve part A. A doublet means both dice show the same number. Looking at all possible outcomes, the doublets are: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). That's 6 doublets out of 36 total outcomes. So the probability of getting a doublet is 6 divided by 36, which simplifies to 1 over 6.
Now let's solve part B. We need outcomes where the sum is greater than 9, which means the sum is 10, 11, or 12. For sum equals 10, we have (4,6), (5,5), and (6,4) - that's 3 outcomes. For sum equals 11, we have (5,6) and (6,5) - that's 2 outcomes. For sum equals 12, we have only (6,6) - that's 1 outcome. Total favorable outcomes are 3 plus 2 plus 1, which equals 6. So the probability is 6 over 36, which simplifies to 1 over 6.
Let's summarize our final answers. 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. Notice that both answers are the same! This happens because both events have exactly 6 favorable outcomes out of 36 total possible outcomes. Remember, probability equals the number of favorable outcomes divided by the total number of outcomes. Great job solving these probability problems!