00:01
Okay, so we know that the probability of a randomly selected box of a certain type of cereal having a prize is 0 .15.
00:08
And we're going to buy until we have three prices.
00:17
Okay? so the first asks, what is the probability that we purchase exactly five boxes? so really what this is asking, right, is what is the probability that the third prize comes on the fifth box? okay, so we know for another way to think of that is what's the probability that i get exactly two prizes in the first four boxes than a prize on the fifth box.
01:05
So the way that i'm going to figure this out is first i'm going to use the binomial probability to figure out what's the probability of getting two prizes in the first four boxes.
01:13
So the binomial theorem is n choose x times the p to the x power times one minus p to the n minus x power.
01:25
So in other words, that's saying how many different ways are there to pick out two prizes out of four boxes times the probability of getting a prize in two boxes and not getting a prize in the other two boxes.
01:42
So that gives us, okay, so we note a 0 .098 chance of this happening, okay, of getting two prizes in the first four boxes.
01:59
But then what's the probability then of getting a prize on the fifth? so i need to take 0 .098 and multiply that times 0 .15.
02:12
And that should give me the probability of purchasing exactly five boxes.
02:19
So 0 .098 times 0 .15 gives me 0 .147 for the probability that i purchase exactly five boxes.
02:33
Okay, so we know that for part b, it asks what is the probability that i have to purchase at least 11 boxes...