00:01
So we have this card game we're playing.
00:03
We're drawing a single card from a 52 car deck.
00:06
And a person has paid $15 to draw jack or queen, $10 for king or an ace.
00:12
And any other card they lose $5.
00:17
So we want to know what the expected gain is.
00:19
So first of all, in the side here, we have the probability of each of the events that we're going to win.
00:27
So probably with jack, probably a queen, probably the king, probably an ace are all four out of 52 because each one of those, types of cards has four in the deck, one for each suit out of the 52.
00:40
There's no overlap here either.
00:42
So if i want to know the probability that we win, now i don't care about the money just yet, it's going to be the probability we draw an ace plus jack, plus glean, plus king, which is going to be 4 over 52 times 4 because there's 4 of the same or 16 over 52.
01:07
We could just add them all together too.
01:13
Now, the probability we lose is going to be one minus that because the only other outcome is we lose.
01:22
So that's going to be 52 over 52 minus 16 over 52, which is 36 over 52.
01:36
Now, what we want to do now is set up our probability distribution table here.
01:42
And there are three possibilities.
01:44
We either win two amounts or lose one amount.
01:46
We'll start with the losing one amount.
01:48
If we don't draw one of those four types of cards, we lose, and the number amount we lose is 5.
01:55
So we're going to express that as negative 5, and the probability we lose is 36 out of 52.
02:05
Next we want to figure out the winnings...