Question

select the correct answer. for a one - week period, three bus routes were observed. the results are shown in the table below. a bus is selected randomly. which event has the highest probability?

	bus route a	bus route b	bus route c	total
delayed	7	8	6	21
total	35	45	30	110

a. the bus is from route c and is delayed.
b. the bus is from route c and is on time.
c. the bus is from route b and is delayed.
d. the bus is from route a and is on time.

Explanation:

Step1: Calculate probabilities for each option

• Probability of a bus being from route C and on - time: $P(\text{Route C and On - Time})=\frac{24}{110}\approx0.218$
• Probability of a bus being from route B and delayed: $P(\text{Route B and Delayed})=\frac{8}{110}\approx0.073$
• Probability of a bus being from route C and delayed: $P(\text{Route C and Delayed})=\frac{6}{110}\approx0.055$
• Probability of a bus being from route A and on - time: $P(\text{Route A and On - Time})=\frac{28}{110}\approx0.255$

Step2: Compare the probabilities

We compare the values $0.255>0.218>0.073>0.055$

Answer:

A. The bus is from route A and is on time.