Question

1. It is estimated that 69 % of all students take economics, 74 % of all students take math, and 52 % of all students take both. Answer the following questions, rounding your answers to two decimal places where appropriate.

(a) What is the probability that a randomly chosen student will take at least one of these courses?  

(b) What is the probability that a randomly chosen student takes economics but not math?

2. Events AA and BB are mutually exclusive. P(A)=0.4 and P(B)=0.6. Find P(A∪B) to one decimal place.

Answer 1

Q.1) Given that, P(economics) = 0.69

P(math) = 0.74 and P(economics AND math) = 0.52

a) We want to find, P(economics OR math)

P(economics OR math)

= P(economics) + P(math) - P(economics AND math)

= 0.69 + 0.74 - 0.52

= 0.91

Therefore, the probability that a randomly chosen student will take at least one of these courses is 0.91

b) We want to find, P(economics AND not math)

P(economics AND not math)

= P(economics) - P(economics AND math)

= 0.69 - 0.52

= 0.17

Therefore, the probability that a randomly chosen student takes economics but not math is 0.17

Q.2) Given that, events A and B are mutually exclusive therefore, $P(A \cap B) = 0$

and P(A) = 0.4, P(B) = 0.6

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$=> P(A \cup B) = 0.4 + 0.6 - 0$

$=> P(A \cup B) = 1.0$