The probability that a person in the United States has type B + blood is 10%. Four un-related people in the United States are selected at random. 1) Find the probability that all fourfour have type B + blood. 2) Find the probability that none of the five have type B + blood. 3) Find the probability that at least one of the five has type B + blood. 4) Which of the events can be considered unusual? Explain. A. None of these events are unusual.

B. The event in part (a) is unusual because its probability is less than or equal to 0.05.

C. The event in part (b) is unusual because its probability is less than or equal to 0.05.

D. The event in part (c) is unusual because its probability is less than or equal to 0.05.

Question

Liana Pierce

Mathematics

5 July, 13:55

The probability that a person in the United States has type B + blood is 10%. Four un-related people in the United States are selected at random. 1) Find the probability that all fourfour have type B + blood. 2) Find the probability that none of the five have type B + blood. 3) Find the probability that at least one of the five has type B + blood. 4) Which of the events can be considered unusual? Explain. A. None of these events are unusual.

B. The event in part (a) is unusual because its probability is less than or equal to 0.05.

C. The event in part (b) is unusual because its probability is less than or equal to 0.05.

D. The event in part (c) is unusual because its probability is less than or equal to 0.05.

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Answers (1)

Know the Answer?

Emily Khan · Answer 1

a. 0.0001

b. 0.6561

c. 0.3439

d. B. The event in part (a) is unusual because its probability is less than or equal to 0.05.

Step-by-step explanation:

a. # We are given that the probability that a person in the United States has Type B + blood = 0.10. Also we are told that four unrelated people in the United States are selected at random.

#We have to find here the probability that all four have type B + blood.

Since the events are independent, we have:

Probability that all four have B + blood = 0.10 x 0.10x 0.10x0.10

= 0.0001

Therefore, the probability that all four have type B + blood is 0.0001

b. We have to find the probability that none have B + blood. Using the complementary law of probability we have:

Probability that blood type is not B + = 1 - 0.10 = 0.90

Therefore, the probability that none have B + blood

= 0.90 x 0.90 x 0.90x0.90=0.6561

Therefore, the probability that none have B + blood is 0.6561

c. We have to find the probability that at least one of the four have B + blood.

#The probability that at least one of the four have B + blood = 1 - Probability that none have B + blood type

=1-0.6561=0.3439

Therefore, the probability that at least one of the four has type B + blood is 0.3439

d. An event is considered unusual if the probability of the event is small or less than 0.05. We note that event a is the only small probabilty and is less than 0.05.

-a is thus considered unusual (the rest are all usual events)