Product Rule of Probability: Probability Regarding AND

Product Rule and Independent Events


They give you the probability of a, b, c, and d in the question.

Part a! They want us to find the probability of a and b. The probability of a and b is simply a probability of times the probability of b which becomes 1 on 24. And that’s it, guys. That’s pretty much the product rule. Before I continue, I just want to point out two important things and that’s all you need to remember for this part. Now remember in the previous one the addition rule, that’s when we have OR, okay?

When we have OR. Probability of say A OR B. Given that there are independent events. They’re not dependent of each other. Then, we can say that it’s the probability of A plus the probability of B. This is what we’ve learned, haven’t we? Just previously. That’s all.

So whenever you see OR, remember that it’s a plus. Addition! That’s why I’ll introduce the addition rule. So don’t think of it too complicatedly. Just remember OR is a plus. Okay? So that’s the first case and the second case is this case here. When the probability of we want to find the probability of A AND B. AND! OR! AND! What do you think will happen here, guys? If it’s and you simply do the probability of times the probability of b and that’s all you need to remember. OR = PLUS. AND = TIMES. Just remember it like that. And that’s pretty much it, okay? So that’s why here. We multiply the two probabilities and we get 1 on 24.

Now b! Probability of a and b and c. So it’s AND. So we multiply, we simply multiply the probabilities a, b, and c just like that and you can calculate that to get 1 on 96.

And c! Find the probability of a and b and c and d. It’s all AND. So you simply multiply them all. Just like this. And then you get that.

Twelve! A class consists of 9 boys and 16 girls. Two of the boys and 4 of the girls are fair-haired. One of the boys is chosen at random and one of the girls is chosen at random. Find the probability that both are fair-haired. Okay! Both are fair-haired. I know that two of the boys, so 2 out of the 9 boys are fair-haired and four, so 4 girls out of the 16 are going to be fair-haired. So those are the probability of each. the individual outcome. So if I want to find the probability of both being fair-haired. I want to find the probability that the boy is fair-haired and the girl is fair-haired. So that’s the probability of the boy being fair-haired, that’s the probability of the girl being fair-haired and because it’s AND. it’s not OR, is it? AND! So we multiply and we just get 1 over 18. Just calculate that yourself and check.

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