A gumball dispenser has 38 orange gumballs, 27 purple ones, and 15 yellow ones. The dispenser operates such that one quarter delivers 1 gumball. (a) Using three quarters, what is the probability of obtaining 3 gumballs in the order orange, purple, orange? b) using 1 quarter, what is the probability of obtaining 1 gumball that is either purple or yellow?

c) using 3 quarters, what is the probability that of the 3 gumballs obtained, exactly 1 will be purple and 1 will be yellow?

Question

Mathematics

Henderson

8 March, 15:43

A gumball dispenser has 38 orange gumballs, 27 purple ones, and 15 yellow ones. The dispenser operates such that one quarter delivers 1 gumball. (a) Using three quarters, what is the probability of obtaining 3 gumballs in the order orange, purple, orange? b) using 1 quarter, what is the probability of obtaining 1 gumball that is either purple or yellow?

c) using 3 quarters, what is the probability that of the 3 gumballs obtained, exactly 1 will be purple and 1 will be yellow?

+2

Answers (1)

Know the Answer?

Flynn · Answer 1

Answer:1). 0.077

2). 0.525

3). 0.09366

Step-by-step explanation:

Total number of balls = 38 orange + 28 purple + 15 yellow = 80 balls.

1). Probability of 3 balls in order of orange, purple, orange.

Probability = (38/80) * (27/79) * (37/78)

=0.475*0.3418*0.474

= 0.077

2). Probability of either purple or yellow

Probability = (27/80) + (15/80)

= 0.525

3). Probability of exactly 1 color each in 3 balls

Probability = 3 ((38*27*15) / (80*79*78))

= 3 * (15390/492969)

=3*0.03122

=0.09366