Homework help?

Hi... So I'm taking statistics as an independent study this summer... Having troubles. I'm on my last question for the night. Can someone walk me through it. I'm having difficulty wrapping my head around it. Please and thank you. Question #4 in the picture. Not asking for the answer, can even discuss a similar problem just need to understand how to get there. Thanks again
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Hi! :welcome: We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

You also appear to have forgotten to attach the picture you're referencing.
Thank you for the link. Still felt like Greek to me. I have an appointment to talk with my professor tomorrow. I have no problem when I have a visual, like flipping a coin or pulling a card from a deck... But for some reason I can't figure out where to start with this problem. I'm figuring out now that independent study wasn't my best option for this class. But thank you again for the link, I really do appreciate it.
Okay, here’s a practical example that illustrates how conditional probability works. Suppose you have an ordinary 52-card deck. If you pick a card at random from the deck, the probability that it’s a heart is ¼ = 0.25. Suppose further that you can’t see the card you’ve drawn but your son tells you it’s a red card. What is the probability that it’s a heart now? (The answer is 13/26 = ½ = 0.5 because there are 26 red cards in a deck, of which 13 are hearts.)

So in this case we can phrase the probabilities as follows:

P(A|B) = P(A & B)/P(B)

(Read: “The probability of A, given that B, is the joint probability of A and B, divided by the probability of B.”)

We let A = “Draw a heart” and B = “Draw a red card”. Then P(A & B) is the probability that it’s a red card and it’s a heart. But if it’s a heart, it’s automatically a red card, so P(A & B) = P(A) = 13/52 = ¼ = 0.25, as before. P(B) is the probability it’s a red card, which is 26/52 = ½ = 0.5. Plugging our values into the above conditional probability formula, we get P(A|B) = P(A & B)/P(B) = ¼/½ = ½ = 0.5.

The gist of it is that in “A, given that B”, knowledge of the occurrence of event B in some way affects the sample space of event A — normally, the sample space of event A is a subset of the sample space of event B.