Addition Rule and Mutually Exclusive Events
Transcript
Okay, if a and b are mutually exclusive, they give you the probability of a and b. They want us to find the probability of a or b. Now, the key thing here is mutually exclusive. What does mutually exclusive mean? Mutually exclusive means the probability of a and b is zero, which means a and b are the outcomes when a and b cannot occur together.
So that’s why probabilities a and b are zero. We don’t have a probability of it because it can never happen. That’s what mutually exclusive means. Make sure you remember what that means because it comes out a lot if I find the probability of a or b. Because p probability of a and b is zero. I don’t have to subtract anything. I subtract zero, which is I don’t need it, right? So the probability of a or b is just the probability of a plus the probability of b. And they give you the outcomes, so they add them together. You should get 5 on 7.
A class consists of nine boys and sixteen girls. two of the boys and four of the girls are glassed. One of the boys is chosen randomly, and one of the girls is chosen randomly. Find the probability that both of them are glassed.
Okay! They give us the probability that two of the boys. So if there are nine um boys and 16 girls, two boys are glassed. And it says four of the girls are glassed. Okay! So the probability that the boy’s glass is 2 out of 9, and the probability that the girl is glassed is 4 out of 16. So it will be something like that because it says both the glassed. For the problem of glassed boy or glassed girl or girl, we add the probability of boy plus the probability of girl and then remember how we subtract the probability of boy and girl both being glassed.
But in this case, the probability of the boy and the girl being glassed together will not happen. We can’t have boy and girl glass together. That’s like not relevant to this part of this question. So we don’t consider the probability of boys and girls both being glassed, okay? So it’s either the boy glassed or the girl glass. They’re independent events. So, therefore, we can’t have them together, that’s why. They’re independent of each other. So that’s why we don’t consider this. This is just zero. It’s like another mutually exclusive event, so, therefore, add up 2 over 9 plus 4 over 16, which is simplified to 17 over 36. Okay? So you can do the calculation.
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