00:01
All right, so we're told that we are playing roulette, and the success, we're going to play 20 times, so we're following a binomial distribution with n of 20 and p of 1 over 38.
00:14
Okay? so, number one asks, what is the probability that we win one time, and that's one time out of 20, right? so if we use the binomial theorem, then it would be 20 choose 1 times 1 over 38 to the first power, because we win 1 .1.
00:32
Time and then we lose the other 19 times.
00:35
So we have a 37 out of 38 chance of losing and that happens 19 times.
00:40
The 20 choose one is because i could win any of the 20 times, right? so i've got 20 times parentheses 1 over 38 times parentheses 37 over 38 to the 19th power, which gets me a probability of 0 .3171, that i win one time.
01:10
For number two, the probability that i win three times, going to be similar.
01:14
It's going to be 20 choose three this time, times 1 over 38 to the third power times 37 over 38.
01:23
I want to lose, i'm going to lose 17 times, right, if i win three times.
01:28
So let me do 20 choose three in my calculator.
01:32
So that is 1 ,140 for this part, okay, times 1 over 38 to the third power times 37 over 38 to the 17th power, which gives me a probability of 0 .0132.
01:55
On the third one, we're told that instead of placing bets on a single number, we're going to place bets on red.
02:04
We're told that there are, are 18 red, 18 black, and two green.
02:11
Okay.
02:12
So that means the probability of winning is going to be 18 over the total number of slots, which there's 38 slots, right? so that will simplify down to 9 over 19 or slightly less than half, right? four asks, what's the probability that if we play six spins, we win exactly three of them...