25. A box contains three good cards and two bad (penalty)...

25. A box contains three good cards and two bad (penalty) cards. Player A chooses a card and then player B chooses a card. Compute the following probabilities: (a) P(A good). (b) P(B good | A good). (c) P(B good | A bad). (d) P(B good ? A good) using (1.5.5). (e) Write out the sample space of ordered pairs and compute P(B good ? A good) and P(B good | A good) directly from definitions. (Note: Assume that the cards are distinct.) (f) P(B good). (g) P(A good | B good).

Transcript

00:01 Okay, so looking at the scenario, probably that a chooses a good card.

00:06 There are three good cards that are total of five, so that's just going to be three out of five for that probability.

00:14 Okay? probably that b is good, or that b is good given a is good.

00:27 So, b good, given a good.

00:30 So if a chooses a good card there's not only two cards left out of the four so it's a one -half probability for the for this case here probably yeah probability of b good given a bad while there's still there's going to be three out of four now because a chose a bad card d probability of be good and a good.

01:09 Okay.

01:09 I just realized i wrote something weird there.

01:12 Be good.

01:14 So d, probability of b good and a good.

01:36 Okay.

01:38 So what we're going to do is we're going to take the probability of b, given that a good, it was good, multiplied by the probability of a being good.

01:45 So three -fifths times one -half, giving me three -tenths.

01:51 Okay, for e, if we want a sample space of order pairs.

01:56 One thing i'm going to do is i'm going to kind of draw out as a bit of a chart here just to get an idea.

02:03 So let's say a has a choice of five cards.

02:05 They're either good, good, good, bad or bad.

02:10 So for here, for b now, b's choice is either going to be good, good, or bad.

02:19 So this pattern repeats two more times.

02:22 If a chooses b or a choose bad and then the b player would have good, good, good or bad at the end so as order pairs, we have 20 possibilities so we have good, good, good, good, good, good, or sorry, good, bad, good bad okay, and we have that two more times so good, good, good, good, good, good...

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