00:01
This fair seven -sided spinner is spun until it lands on green, or until it has spun five times in total.
00:09
And we are asked to find the probability distribution for the random variable x, which is the number of times the spinner is spun.
00:18
So first of all, on any individual spin, the probability that it lands on green is four out of seven, because there are four green sectors and a total of seven sectors.
00:35
So we want to make a probability distribution, and it's going to go up to five, because the game or the spinning ends once we've hit five spins, or it ends if we hit green before that.
01:04
So for the probability, well, there's not going to be zero, it has to be one.
01:09
So the probability that x is equal to one is p, the probability of getting green on the first spin, the probability that x equals 2 is 1 minus p, the first spin is not green, times p.
01:28
Second spin is green, this is 12 forty -ninths.
01:43
For x equals 3, first two spins have to be not green, third spin is green, this is 36 over 343.
02:04
As you might have detected, there's a pattern here.
02:11
The factor 1 minus p is to the power x minus 1...