Question

The probability that it rains is about 20%.

The probability that the bus is late is about 8%.
The probability that it rains and the bus is late is about 3%.
The probability that the train is late is about 5%.
The probability that it rains and the train is late is about 1%.

6. To decide whether the rain and the train running late are dependent or independent events, first define the two events and then write their probabilities as decimals. (3 points) Let event A = ________________________. P(A) = ______. Let event B = ________________________. P(B) = ______. A and B = ________________________. P(A and B) = ______. 7. Use the probabilities from question 6 to decide whether the rain and the train running late are independent or dependent events. (2 points: 1 point for the correct math, 1 point for the conclusion)

Answer 1

The two are independent.

Explanation:

Answer 2

Explanation:

Let A= probability it rains

P(A)=0.2

Let B be the probability that the train is late = 0.05

P(B)=0.05

A and B is A∩B= the probability it rains and the bus is late =0.01

probability pf (A and B)=0.01

7) independent events are related by expression:

A∩B=P(A)*P(B)

=0.2*0.05=0.01

check :

p(A|B)=P(A∩B)÷P(B)=0.01/0.05= 0.2

the two event are independent