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Person that has AO blood will have baby With person that has BB blood what i5 the probability that the baby will have AB blood? (Notice that thetc arc no lowcr case...

Question

Person that has AO blood will have baby With person that has BB blood what i5 the probability that the baby will have AB blood? (Notice that thetc arc no lowcr case lettcfs because they are all dotinant)AA:AO:AB:BO:

person that has AO blood will have baby With person that has BB blood what i5 the probability that the baby will have AB blood? (Notice that thetc arc no lowcr case lettcfs because they are all dotinant) AA: AO: AB: BO:



Answers

What is the likelihood that a parent with Type AB blood would have a child with Type O blood? a. $50 \%$ b. $25 \%$ c. $0 \%$ d. This can't be determined without knowing the blood type of the other parent.

In this exercise, we're told that 4% of people have type A B blood so we can consider each person to be a Bernoulli trial. Where success is having a baby blood and failure is not having type baby blood. Each person is independent because the probability for somebody having type A B blood ah is not dependent on the outcome for other people. For part, A were asked, on average, how many donors must be checked to find someone with Type A B blood? So if we define success as somebody having a B blood type A B blood, we know that the probability of success is 0.4 from the question. And if we define X as the number of blood donors until we find Type A B blood, then we can say X is a geometric random variable with probability of success of 0.4 And we know that for a geometric random variable, the expected number of trials until success is equal to one over P here that is equal to one over a 0.4 and that comes out to 25. So on average, we would expect to have to look at 25 donors of blood before we find one with Type A B blood now for Part B were asked, What is the probability that there is a Type A B donor among the first five people that we check? So in this case, let's define X as the number of successes in five trials where success is defined as a person having type A B blood. So if we want to know the probability of success that there is a Type A B donor in five people, Random variable X is a by normal binomial random variable based on five trials and probability of success of 0.4 So we're looking for the probability of a person with type baby blood means at least one person, so that's equal to one, minus the probability of no person in five having type 80 blood. It's one minus. So using the formula or the probability mass function for binomial random variables, be five. Choose zero time 0.4 to the exponents zero time, zero point 96 to the export and five and this comes out to 0.185 So if we check five donors, the probability of having a person with Type A B blood among those five donors is about 18.5%. Part C were asked the probability that the first type A B blood donor will be found among the first six people. So if we once again defined X as the number of successes, except it's the number of successes in six trials as time because we're looking at six people, then excess still a binomial random variable but based on six trials. So if we're looking for the probability that the first type A B donor is found among the first six people, this is the same is asking What is the probability that there is at least one person with Type A B blood among the first six people? Because as long as there is at least one person with Type B blood donor, then we know that the first person with Type A B was among the first six people. If there is at least one type A B blood donor among the six, then we know that the first type A B blood donor must have been among the six. So, really, once again, we're looking for the probability of at least one success, and this is equal to one minus 6 to 0. 0.4 exponents zero 0.962 exponents six and it comes out to 0.217 So the probability that the first type A B donor will be found among the first six people is about 21.7%. And for party were asked what the probability is that we will not find a Type A B donor before the 10th person so before the 10th person means within the first nine trials within the first nine people. So Anna's equal to nine. So here we can define X as the number of successes in the first in nine trials. And not finding a donor with Taipei de blood in those nine trials is the probability that X is equal to zero. Here. X is a binomial random variable based on nine trails and probability success of 0.4 and similar to the calculations in part C and B, this one comes out to you zero point 693

Okay, So for this problem, we're looking at these different blood types and were given a few different probabilities associated with that part. A access to find the missing probability in this table, the probability of getting blood Type A B. Now, when we're talking about probability in total probability, we all of our probabilities add upto one. So I can just start off by saying 10.49 plus 0.27 plus 0.20 Now, whenever I obviously together, those will give me up all the probabilities combine of O and B, but not a B. So I have to add in probability of a B, and he should all add up to one. So I do. You 10.49 point 27 plus point to this gives me 0.96 plus probability of a B that you needs out of the one and using algebra. I knew that my probability my missing probability of a B is 10.4 So right here is 0.4 That's the only thing that will make this legitimate. Now, Looking at Part B says was the probability that person chosen does not have type A B blood. Well, if it's not a B blood than it has to be Oh, a or B. So looking back, we already did that when we were trying to figure that out. That's thes three probably is combined, so probably of not being a B, which is also known as the probably A B compliment, is 30.96 So for part A, we have 0.4 and part B. We have 0.96 now, it says for part C. Maria has type B blood, and she can safely received blood transfusions from people with blood type O and B. That was the probability that that a randomly chosen black American can donate blood to Maria. So we need to figure out she can get blood from types. Oh, and types B. So if we're trying to figure out the probability that someone randomly chosen can't donate, then what's the probably that that randomly chosen person has either type O or type B. So open up a page. So we need to look at the probability of O union with B this capital you in the middle here represents union. That means O or B. So we're gonna be looking at this and this. So 0.49 plus 0.249 plus point to which gives me an answer. 0.0.69 that's what we're looking for.

For this question, we can make multiple opponents squares to figure out the final genetic makeup of the Children. So here we have the father, the mother, and we'll just call the mother's father, the grandfather. And finally, we are looking for the offspring. So the father's genetic makeup is a B. The mothers is be with some sort of other Alil. And the grandfather is oh, so first, If we're looking for this unknown second olio of the mother, we can perform a cross between the grandfather and the mother. Since we know the mother of that mother or the grandmother has to express some sort of variation of the B trait, the mother can be either b, o or B. So make it be over this circumstance. So here we can do the Planet Square Cross and we find out that the only genetic makeup for the mother of interest is going to be this B o group. Because if the mother expressed oh oh, her blood type would be Oh, rather than be so here. We know that the mother's genotype is going to be B o. From there, we can do our second upon its square between the A B father and the B O Mother. So here we can write a B B o have a baby, B, B, A O and B O. If we write out the phenotype for each of these, there's a 25% chance the child will be a B. There is a 25% chance for BB, 25% chance for B O and 25% chance for a Oh, so here we can just combine the B, B and B O. This would be a 50% chance they would be the blood type B. It would be the 25% chance for a B and 25% chance for a of course, because there's no oh grouping. There's 0% chance for the child to express Justin. Oh, Fino type. So here, the best answer choice for this question is going to be D that they have this 25% for the A B, 50% for be and 25% for oh,

We have a woman who is type A B. So the woman is a B, and she has a baby who has type B blood. That's on Lee know about it. And there are two possible fathers and were being asked whether or not we can figure out if either one of these guys is the father. Um, the answer's no, we really can't tell. The reason has to do with, uh, just the limited information we have. So a father one is has a type blood, and what that means is that he could either be a oh or a A. In this case, the B Lille could come from the mother and the O If he does have a no could have coming from this father, the other potential father instead of in the same situation. We know he has be blood, but we don't know if it's because he has the B and then the little IA Leo, Um, or if he is, uh, be be right in this case, right for the baby. In this scenario, the baby, of course, is still be right. And the baby could have gotten the be Leo from its mother and again, it could have gotten a little I a Leo, um, from this father. So we don't know the exact Jima types of the father, But this plant there's and there's no easy way to discern which is the father. Um, if we could get the exact, uh, genotype of the father, for example, if we knew that this father was a that wouldn't be important. If we know this father was BB, that would be informed. And of course, we'd like to know more about me. So at this point, there's no way to tell.


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