(HINT: this problem is similar to the practice exercise on Java and C++ programm

Question

(HINT: this problem is similar to the practice exercise on Java and C++ programmers…) A recent study estimated that 40% of adults get enough sleep, 46% get enough exercise and 24% do both. Find the probabilities of the following events:

a) What is the probability that an adult gets enough sleep and not enough exercise?

b) What is the probability that an adult gets not enough sleep but enough exercise?

c) What is the probability that an adult does not get enough sleep and enough exercise?

d) Explain what probability rules you used to answer the questions above

Explanation / Answer

E = Adults that get enough sleep

F = Adults that get enough exercise

P(E) = 0.40P(F) = 0.46P(E F) = 0.24

(a)P(E Fc)+ P(E F) = P(E) =>P(E Fc)=P(E) - P(E F) = 0.40 - 0.24 =0.16

(b)P(Ec F)+ P(E F) = P(F) =>P(Ec F)=P(F) - P(E F) = 0.46 - 0.24 =0.22

(c)P(Ec Fc)= P[(E U F)c] = 1 - P(E U F) = 1 - (0.40 + 0.46 - 0.24) =0.38

(d)Low of the complement in combination with addition rule

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