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)

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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)

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

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