00:01
So in this question, we're playing for four hours at a rate of 60 hands per hour.
00:07
So four hours, 60 hands per hour gives n equals 60 times four, which is 240 hands.
00:22
So now the number of hands, so the probability of winning a hand, p is 0 .49 probability of winning a hand.
00:41
And then if you win, then, so we're betting $50.
00:51
So if we lose, we lose $50.
01:00
So we win minus $50 if we lose the hand.
01:05
And if we win the hand, then you'll win $50.
01:22
So that means that your total number of winnings.
01:26
So total winnings, w total, is going to.
01:30
Be the number of hands you is going to be $50 times the number of hands you win minus the number of hands you lose, which is $50 times the total number of hands.
01:47
So because the number of hands you lose is the total number of hands minus the number of hands you win.
01:52
So that's twice the number of hands you win minus the total number of hands.
01:58
So this is $100 times the number of hands you win minus n which is 240 so 240 times 50 is $12 ,000.
02:13
So that's your total winnings.
02:17
So now what, so now how many hands do you expect to win? well, you have a 50 % so n equals 240 hands.
02:38
Probability of winning is 0 .49.
02:40
So the number of of hands you win is going to be binomially distributed with n equals 240 and p is 0 .49 and that means the expected number of hands that you win is going to be 240 times 0 .49 which is 117 .6 so the expected winnings is going to be a hundred times that minus 12 ,000 which is minus 240 dollars so what is the probability that you lose $1 ,000 or more? so that's the probability that your total winnings is less than minus $1 ,000.
03:31
Well, your total winnings is.....