00:01
In this problem, we have a roulette wheel and there are 38 numbers on it, 1 through 36, a 0 and a double 0.
00:09
Now, if a man always bets that the outcome will be one of the numbers 1 through 12, then we need to determine a few probabilities.
00:16
Now, the first probability is that the man will lose his first 5 bets.
00:21
Now, note that winning and losing the bets, these are all independent of each other.
00:27
That is whether or not he wins or loses in one bet that does not affect in any way or form whether or not he loses or wins the next bet or the other bets.
00:36
So they are all independent.
00:39
And as a result, the probability that he will lose his first five bets will just be the probability that he loses one bet to the power five.
00:48
And what is the probability that he loses one bet? that will be the number of favorable outcomes divided by the total number of outcomes.
00:55
There are 38 numbers.
00:56
So the total number of outcomes is 38 and that's for losing out of 38 numbers he will win the bet if the outcome is any of the numbers 1 through 12 so he will lose it if we get any of the other numbers so that's 38 minus 12 which is equal to 26 losing outcomes so the number of favorable outcomes will be 26.
01:18
So the probability that he loses his first 5 bets that will be 26 by 38 whole to the power 5 and the value of this is approximately equal to 0 .15...