Question

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?

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