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Causes of death. Government data assign a single cause for each death
that occurs in the United States. The data show that the probability is 0.34 that
a randomly chosen death was due to heart disease, and 0.23 that it was due to
cancer. What is the probability that a death was due either to heart disease or
to cancer? What is the probability that the death was due to some other cause?

18.8 High school academic rank. Select a first-year college student at ran-
dom and ask what his or her academic rank was in high school. Here are the
probabilities, based on proportions from a large sample survey of first-year stu-
dents:
Rank: Top 20% Second 20% Third 20% Fourth 20% Lowest 20%
Probability: 0.44 0.26 0.23 0.06 0.01
(a) What is the sum of these probabilities? Why do you expect the sum to have
this value?
(b) What is the probability that a randomly chosen first-year college student
was not in the top 20% of his or her high school class?
(c) What is the probability that a first-year student was in the top 40% in high
school?

Respuesta :

Mistadijex

Answer:

1a.) 0.4918

1b.) 0.5082

2a.) 1

2b.) 0.56

2c.) 0.70

Step-by-step explanation:

probability that death was caused by a heart disease = p(H) = 0.34

probability that death was caused by cancer p(C)= 0.23

For question 1a,

Probability that death was caused by either heart disease or cancer = p(H) + p(C) - [p(H) * p(C)

= 0.34 + 0.23 - (0.34*0.23)

= 0.57 - 0.0782

= 0.4918.

1b.) Probability that death was caused by other cause = 1 - [probability that death was caused by heart failure or cancer

= 1 - 0.4918

= 0.5082

For question 2,

a.) Sum of all the probabilities = 0.44 + 0.26 + 0.23 + 0.06 + 0.01 = 1

The sum is 1 because the Sum of the probabilities of all outcomes of an event must be equal to 1.

b.) Probability that a randomly chosen first year student was NOT part of top 20% = 1 - [probability that. Randomly chosen first year student was in top 20%]

= 1 - 0.44

= 0.56

C.) probability that Student was in top 40% = 0.44 + 0.26

=0.70

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