22. A company is planning to expand its operations. They are currently considering 9
different locations. Two of these are in Ohio. If the locations are selected at random
from the 9 locations being considered, the probability of selecting the two sites in Ohio
is
(a) 0.056
(b) 0.028
(c) 0.045
(d) 0.036
23. From a bag containing 10 white and 5 red balls, a ball a ball is drawn at random. The
probability that the ball is red is:
(a) 1/4
(b) 1 /2
(c) 1/3
(d) 1/15
To solve both of these probability questions, we need to use the concept of "probability of an event" which is the number of favorable outcomes divided by the total number of possible outcomes.
For question 22:
We have 9 different locations, 2 of which are in Ohio. The probability of selecting the two sites in Ohio can be calculated as follows:
Total number of possible outcomes = number of ways to select 2 out of 9 locations = 9C2 = (9!)/(2!(9-2)!) = 36
Number of favorable outcomes = number of ways to select 2 out of 2 Ohio locations = 2C2 = 1
Probability = Number of favorable outcomes / Total number of possible outcomes = 1/36
So, the correct answer is not given as an option. None of the provided options (a), (b), (c), or (d) are correct.
For question 23:
We have a bag containing 10 white balls and 5 red balls. The probability of drawing a red ball can be calculated as follows:
Total number of possible outcomes = number of balls in the bag = 10 + 5 = 15
Number of favorable outcomes = number of red balls = 5
Probability = Number of favorable outcomes / Total number of possible outcomes = 5/15 = 1/3
So, the correct answer is (c) 1/3.