Question

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events: = chocolate chosen = strawberry chosen = vanilla chosen = ice cream on a cone ice cream in a cup Find the probability that the ice cream was sold in a cup and was strawberry flavor. Place your answer, rounded to 2 decimal places, in the blank. For example, 0.34 would be a legitimate entry.

Answer 1

See explanation

Explanation:

Given:

Chocolate = 45% (or 0.45 as decimal)

Strawberry = 30% (or 0.30 as decimal)

Vanilla = 100% - 45% - 30% = 25% (or 0.25 as decimal)

Cones:

Chocolate = 75% (or 0.75 as decimal)

Strawberry = 60% (or 0.60 as decimal)

Vanilla = 40% (or 0.40 as decimal)

Cups:

Chocolate = 100% - 75% = 25% (or 0.25 as decimal)

Strawberry = 100% - 60% = 40% (or 0.40 as decimal)

Vanilla = 100% - 40% = 60% (or 0.60 as decimal)

Hence, probabilities of events:

Chocolate chosen
`=0.45`

Strawberry chosen
`=0.30`

Vanilla chosen
`=0.25`

Ice cream on a cone
`=0.45\cdot 0.75+0.30\cdot 0.60+0.25\cdot 0.40=0.6175\approx 0.62`

Ice cream in a cup
`=0.45\cdot 0.25+0.30\cdot 0.40+0.25\cdot 0.60=0.3825\approx 0.38`

The probability that the ice cream was sold in a cup and was strawberry flavor is

`P=0.30\cdot 0.40=0.12`