00:01
In a bag, we have 12 red balls labeled with numbers 1 through 12, and we have 7 white balls labeled 13 through 19.
00:11
And for part a, we're asked for the probability that the ball, drawn randomly from the bag, is not even numbered.
00:28
So this is equal to the probability that it is odd numbered.
00:35
And here we can use the classic approach to probability, which says that the probability of a given event, in this case the probability that the ball selected is odd is equal to the number of outcomes in the sample space that satisfy that event divided by the total number of outcomes in the sample space.
00:56
So here the total number of outcomes is any one of the 19 balls.
01:01
So there's a total of 19.
01:03
And the number of outcomes which result in an odd number are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
01:15
So this probability is 10 over 19, which is equal to approximately .5263.
01:26
And then for part b, we're asked for the probability that the ball is red and even numbered.
01:44
So we can use the same strategy as for part a.
01:49
Here the denominator is the same.
01:51
There's 19 ways to choose one ball out of 19.
01:55
Now the number of balls that could be drawn that are both red and even.
02:00
So that's everything in the red category that's an even number.
02:04
So we have 1, 2, 3, 4, 5, 6.
02:11
And this comes out to approximately .3158...