Among persons donating blood to a clinic, 80% are Rh-(that is, they have the Rhe

Question

Among persons donating blood to a clinic, 80% are Rh-(that is, they have the Rhesus factor present in their blood). Five people donate blood at the clinic on a particular day 7. a. Find the probability that at least one of the five does not have the Rh factor. b. Find the probability that at most four of the five have Rh blood. A survey of 100 people revealed: 15 enjoy only scary movies 30 enjoy only comedy films 8. 48 enjoy watching both types 7 do not watch movies Let A denote the event that a randomly chosen survey participant enjoys scary movies, and B denotes the event that the participant enjoys comedies. Calculate the following probabilities a. P(A) b. P(AUB) c. P(B) e. P(AUB) f. P(AB) g. P(A UB)

Explanation / Answer

7. a. Let us calculate the probability that none of the five have Rh factor

Probability that a person has Rh factor = 80% = 0.8

=> Probability that all five people have Rh factor = (0.8)5

Therefore, the probability that atleast one person does not have Rh factor = 1 - (0.8)5

= 1 - 0.32768

= 0.67232

b. This question is the same as a.

The answer is 0.67232.

8. Given P(U) = 100 P(A-B) = 15 P(A B) = 48 P(B-A) = 30 P(A U B)' = 7

a. P(A) = P(A-B) + P(A B) = 15 + 48 = 63

b. P(A U B) = P(U) - P(A U B)' = 100 - 7 = 93

c. P(B) = P(B-A) + P(A B) = 30 + 48 = 78

P(B') = U - P(B) = 100 - 78 = 22

d. P(A B') + P(A B) = P(A)

=> P(A B') + 48 = 63

=> P(A B') = 63 - 48 = 15

P(A U B') = P(A) + P(B') - P(A B')

=> P(A U B') = 63 + 22 - 15 = 70

f. P(AB)' = P(A B)' = U - P(A B)

= 100 - 48 = 52

g. P(A U B)' = 7

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