Addition Rule and Mutually Exclusive Events

Transcript

Okay, if a and b are mutually exclusive and they give you what probability of a and probability of b is. 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 means the outcomes for when a and b cannot occur together.

So that’s why probability a and b are zero. We don’t have a probability for 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. Therefore if I find 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 really need it, right? So probability of a or b, in this case, is just the probability of a plus the probability of b. And they give you the outcomes, so they just add it 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 at random and one of the girls is chosen at random. Find the probability that both of them are glassed.

Okay! They give us the probability that two of the boys. So if there’s nine um boys and 16 girls, two of the boys are glassed. And it says four of the girls are glassed. Okay! So the probability that the boy’s glass is 2 of 9 and the probability that the girl is glassed is 4 out of 16. So it’s going to be something like that. Because it says both the glassed. 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 is not going to 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 boy and girl both being glassed, okay? So it’s either the boy glassed or other 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 and murray.

 

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