3. Four blood types O, A, B and AB occur in the population...

3. Four blood types O, A, B and AB occur in the population with frequencies 0.45, 0.4, 0.1, and 0.05 respectively. Within all the blood types, the Rh factors, plus and minus, occur with frequencies 0.85 and 0.15 respectively. Find the probability that a randomly selected person has: (a) type A and Rh+ (b) type O and Rh- (c) Blood is needed for a person of type A and Rh+. A donor must have type A or O with the same Rh factor. What is the probability that a suitable donor will be found among five randomly selected persons? (Hint: Consider the event that none of the five donors is suitable.)

Transcript

00:01 So we have people have one or four different blood types, o, a, b, and ab at the given percentages in the table.

00:08 So we need to know the following probabilities.

00:11 What is the probability that a randomly selected blood type is not b? well, if 10 % are b, then 100 % minus the 10 % are not b, so we're looking at 90%.

00:25 So let's look at b.

00:26 Among four random people, what is the probability that they all have a? so we're looking at four people.

00:35 The probability of them having a is going to be 37%.

00:38 So we're going to put that as 0 .37 for all three.

00:43 And what we have to do is multiply those together.

00:47 So if we go to our calculator and get 0 .37 to the fourth power, that's going to be the probability.

00:53 So now, none of them are type b.

00:58 So for none of them being type b, the same four people.

01:02 Well, remember, we figured out how many were not b here.

01:05 So not b would be each one of these values, and that we would simply have 0 .9 to the fourth.

01:14 So what is the probability that at least one person is type o? so at least one.

01:21 Now, that means we could have 1, two, three, or four.

01:30 So we can have one, two, three, or four.

01:34 Now the only other option is that none of them have type o.

01:39 So we want to, if we figure out how many, the probability of none, we can subtract that from one and we'd have the probability of one, two, three, or four...

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