Question

Ten percent of a company's total output consists of baseballs, 10% consists of softballs, and 15% consists of tennis balls. Its only remaining product is handballs. If we place balls in a box in the same ratios as the company's output and select a ball at random from the box, what is the probability of the following? (Enter your probabilities as fractions.)

(a) the ball is a baseball
(b) the ball is a tennis ball
(c) the ball is not a softball (d) the ball is a handball

Answer 1

a) 10% (baseballs) / 35% (total) = 2/7

b)15% (tennis balls) / 35% (total) = 3/7

c) 100% - 10% (softballs) = 90%

d) 100% - 10% (baseballs) - 10% (softballs) - 15% (tennis balls) = 65%

Step-by-step explanation:

(a) To find the probability that the ball is a baseball, we first need to add up the percentages of baseballs, softballs, and tennis balls to get the total percentage:

10% (baseballs) + 10% (softballs) + 15% (tennis balls) = 35%

So, 35% of the company's output consists of one of these three types of balls. Since 10% of that output consists of baseballs, we can find the probability of selecting a baseball by dividing the percentage of baseballs by the total percentage:

10% (baseballs) / 35% (total) = 2/7

Therefore, the probability of selecting a baseball is 2/7.

(b) Similarly, to find the probability that the ball is a tennis ball, we divide the percentage of tennis balls by the total percentage:

15% (tennis balls) / 35% (total) = 3/7

Therefore, the probability of selecting a tennis ball is 3/7.

(c) To find the probability that the ball is not a softball, we need to subtract the percentage of softballs from 100% (since there are no other types of balls besides these four):

100% - 10% (softballs) = 90%

Therefore, the probability of selecting a ball that is not a softball is 90%.

(d) Since the company's remaining product is handballs, we know that the percentage of handballs is:

100% - 10% (baseballs) - 10% (softballs) - 15% (tennis balls) = 65%

Therefore, the probability of selecting a handball is 65%.