24. Suppose there are five traffic lights that you need to pass while driving from your work to
school. The probabilities that you will stop for these red lights are: 0 red light with
probability 0.05, 1 red light with probability 0.45, 2 red lights with probability 0.30, 3 red
lights with probability 0.12, 4 red lights with probability 0.06, 5 red lights with probability
0.02. The probability that you stop for at least two red lights on a given day
(a) 0.20
(b) 0.30
(c) 0.50
(d) 1.00
25. A survey was conducted to learn about the shopping preference of consumers during
holiday season. Out of 2000 respondents 22% said they would prefer to shop online
because of the free shipping offered; 45% said that they would like to shop in malls and
discount outlets while 15% of the shoppers said they would use both. The probability
that a randomly selected shopper would use at least one method of shopping is
(a) 0.67
(b) 0.82
(c) 0.60
(d) 0.52
To solve these probability questions, we need to use basic probability principles.
For question 24:
We are given the probabilities of stopping at different numbers of red lights. To find the probability of stopping at least two red lights, we need to calculate the sum of the probabilities of stopping at 2, 3, 4, and 5 red lights.
Probability of stopping at 2 red lights = 0.30
Probability of stopping at 3 red lights = 0.12
Probability of stopping at 4 red lights = 0.06
Probability of stopping at 5 red lights = 0.02
Sum of these probabilities = 0.30 + 0.12 + 0.06 + 0.02 = 0.50
So, the probability of stopping at least two red lights is 0.50. Therefore, the correct answer is (c) 0.50.
For question 25:
We are given the percentages of shoppers using different methods of shopping. To find the probability of a randomly selected shopper using at least one method of shopping, we need to subtract the percentage of shoppers who do not use any method from 1.
Percentage of shoppers using online shopping = 22%
Percentage of shoppers using malls and discount outlets = 45%
Percentage of shoppers using both methods = 15%
Percentage of shoppers not using any method = 100% - (22% + 45% - 15%) = 100% - 62% = 38%
So, the probability of a randomly selected shopper using at least one method of shopping is 1 - 0.38 = 0.62. Therefore, the correct answer is (c) 0.60.