Suppose that you and a friend are playing cards and you...

Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are diamonds, your friend will pay you $615. Otherwise, you have to pay your friend $37. Step 2 of 2 : If this same bet is made 621 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.

Transcript

00:01 You and a friend are having a wager.

00:03 So you're going to be picking two cards without replacement from a deck.

00:07 If you are both diamonds, you get 615.

00:10 So i'm going to make a little column here.

00:12 You can either win 615, or you can lose 37.

00:17 Okay, so what we're going to do is start by finding the expected value of this distribution, and then we'll apply it to the case where you play 621 times.

00:28 So we need the probability of each of these happening.

00:30 What's the probability of getting two diamonds without replacement? so the first one, well, there are 13 diamonds out of the 52 cards in a deck.

00:42 So the probability your first card is diamonds is 13 out of 52.

00:47 For the second card, well, it's without replacement, so there's only 51 cards left.

00:52 And of those, only 12 are diamonds, because you already take one out.

00:57 And you would multiply these to get the total probability.

01:01 So i'm just going to put this.

01:03 Here.

01:04 That's the probability of winning, and 1 minus this, which i'll just put p, is the probability of losing.

01:12 I'm keeping it like this to try and avoid any rounding errors when i actually calculate this.

01:18 So the expected value of the bet, what you expect to get if you play once on average, you take each value of x, you multiply by its probability, you add them up.

01:33 So let's do that...

Question

Please give Ace some feedback