Question

In: Statistics and Probability

2. The blood groups of 200 people is distributed as follows: 74 type A, 26 type...

2. The blood groups of 200 people is distributed as follows: 74 type A, 26 type B, 88 type O, and 12 type AB. With this information, answer the following four (3) questions.

Please leave answers to four (4) decimal places!

a. What is the probability of randomly selecting a person has O blood type or AB blood type out of the blood group? (1 point)

continued next page….

…continued from last page

b. What is the probability of selecting out two consecutive people have B blood type in a row (with replacement)? (1 point)

c. What is the probability of selecting out a person has A blood type and afterwards selecting out another person has B blood type out of the blood group (without replacement)? (1 point)

Solutions

Expert Solution

a . The probability of randomly selecting a person has O blood type or AB blood type out of the blood group is 0.5

b. The probability of selecting out two consecutive people have B blood type in a row (with replacement) is 0.0169

c. The probability of selecting out a person has A blood type and afterwards selecting out another person has B blood type out of the blood group (without replacement) is 0.0483

The complete solution of above part a. to c. are as below

The blood groups of 200 people is distributed as follows: 74 type A, 26 type B, 88 type O, and 12 type AB

The number of people of different blood groups are

type A blood groups = 74

type B blood groups = 26

type O blood groups = 88

type AB blood groups = 12

n = total number of people of all blood groups = 200

The probabilities of the people of the different blood groups

P(A) = 74/200, P(B) = 26/200, P(O) = 88/200, P(AB) = 12/200

a. We find the probability of randomly selecting a person has O blood type or AB blood type out of the blood group.

Using addition theorem

P(O(AB)) = P(O) + P(AB) - P(O(AB))

Here, O(AB) =

P(O(AB)) = 0

Using the all values we get P(O(AB))

P(O(AB)) = 88/200 + 12/200 - 0

P(O(AB)) = 0.5

The probability of randomly selecting a person has O blood type or AB blood type out of the blood group is 0.5

b. We have to the probability of selecting out two consecutive people have B blood type in a row (with replacement)

The selection of two consecutive people have B blood type in a row is an independent

= P(B) * P(B)

= (26/200) * (26/200)

= 0.0169

The probability of selecting out two consecutive people have B blood type in a row (with replacement) is 0.0169

c. We have to find the probability of selecting out a person has A blood type and afterwards selecting out another person has B blood type out of the blood group (without replacement)

Using without replacement the selected units are not replaced into population, that is sample size decreases trial to trial.

The probability of selecting out a person has A blood type = P(A) = 74/200-----(1)

afterwards The probability of selecting out another person has B blood type out of the blood group using 199 people.

The probability of selecting out another person has B blood type = P(B) = 26/199------(2)

The above selction of people are an independent of each other.

The probability of selecting out a person has A blood type and afterwards selecting out another person has B blood type out of the blood group (without replacement)

= (74/200) * (26/199) (By equation (1) and (2))

= 0.0483

The probability of selecting out a person has A blood type and afterwards selecting out another person has B blood type out of the blood group (without replacement) is 0.0483

Summary :-

a . The probability of randomly selecting a person has O blood type or AB blood type out of the blood group is 0.5

b. The probability of selecting out two consecutive people have B blood type in a row (with replacement) is 0.0169

c. The probability of selecting out a person has A blood type and afterwards selecting out another person has B blood type out of the blood group (without replacement) is 0.0483

orchestra answered 1 year ago

Next > < Previous

Related Solutions

In the US, 44.3% of all people have type O blood, 41% have type A blood,...

In the US, 44.3% of all people have type O blood, 41% have type A blood, 10.2% have type B blood and 4.5% have type AB blood. A researcher wants to see if the distribution of blood type is different for millionaires. The table below shows the results of a random sample of 2864 millionaires. What can be concluded at the αα = 0.01 significance level? Complete the table by filling in the expected frequencies. Round to the nearest whole...

A sample of 200 individuals are tested for their blood type is given in the first...

A sample of 200 individuals are tested for their blood type is given in the first table, and the results are used to test the hypothesized distribution of blood types. The observed results are given in the second table. At the .05 level of significance, is there sufficient evidence to show that the stated distribution is incorrect? Blood Type Â Â A Â Â Â Â B Â Â Â Â O Â Â Â Â AB Â Â Percent...

We have reason (somehow) to believe that 34% of people have blood type A, 15% blood...

We have reason (somehow) to believe that 34% of people have blood type A, 15% blood type B, 23% blood type AB, and 28% blood type O. We go out and collect a sample of 100 people, and find the following: A: 12 B: 56 AB: 2 O: 30 a. Present the data that was collected by this researcher in an appropriate graphical form. Be sure to label your graph appropriately and to give it an appropriate title. b. Test...

“1. What determines blood type? “ Click here to enter text. “2. What type of blood...

“1. What determines blood type? “ Click here to enter text. “2. What type of blood antigens are expressed if a person is blood type AB negative? “ Click here to enter text. “3. Why doesn’t a transfusion reaction occur the first time an Rh negative patient is exposed to Rh positive blood? “ Click here to enter text. What surprised you about the anatomy of the sheep’s heart? Click here to enter text. Research diseases of the heart valves....

3. 28% of the population has high blood pressure. in a random sample of 200 people,...

3. 28% of the population has high blood pressure. in a random sample of 200 people, what is the exact probability (to 7 decimal places) that A. less then 65 people have high blood pressure B. more then 30, but less then 54, of the people selected have high blood pressure C. more then 140 people do not have high blood pressure? D. answer B using normal approximation to the binomial, remembering to use the continuity correction. use the pnorm...

How could epidemics be responsible for the variations on blood type of different people across the...

How could epidemics be responsible for the variations on blood type of different people across the globe?

Blood type AB is found in only 3% of the population.† If 235 people are chosen...

Blood type AB is found in only 3% of the population.† If 235 people are chosen at random, find the probability of the following. (Use the normal approximation. Round your answers to four decimal places.) (a) 5 or more will have this blood type .8365 Correct: Your answer is correct. (b) between 5 and 10 will have this blood type

In a sample of 674 people, 25 had type AB blood and the rest ( 674...

In a sample of 674 people, 25 had type AB blood and the rest ( 674 minus 25) had some other type. We are interested in a 95% confidence interval for the proportion of all people who have type AB blood. The error bound is?

A certain rare blood type can be found in only 0.05% of people. If the population...

A certain rare blood type can be found in only 0.05% of people. If the population of a randomly selected group is 3000, Find the probability that two persons in the group have this rare blood type. 1 person in the group has this rare blood type. at least two persons in the group have this rare blood type.

1-What is true of people with O blood type? A) They possess an enzyme the adds...

1-What is true of people with O blood type? A) They possess an enzyme the adds a phospholipid to the surface of red blood cells B) They possess an enzyme that adds galactose to glycolipids the surface of red blood cells. C) They possess an enzyme the adds N-acetyl glucosamine to glycolipids on the surface of red blood cells. D) They lack an enzyme that adds a sugar molecule to glycolipids on the surface of red blood cells. 2-Which of...

Subjects