Question

50 POINTS !!!!

Fran has a bag with 20 marbles in it. Some of the marbles are blue, some are green, and some are yellow.

She draws one marble at random, records the color, and returns it to the bag.
Here is her data after 1200 trials:


Blue 845

Green 305

Yellow 50

Estimate the probability that a marble drawn at random will be blue.
Estimate the probability that a marble drawn at random will be green.
Estimate the probability that a marble drawn at random will be yellow.

Express each probability estimate as a fraction with 20 in the denominator.

Answer 1

Prob(of a blue) = 845/1200 = 168/240

Prob ( green) = 305 / 1200 = 61/240

Prob ( yellow) = 1/24

Answer 2

Our initial estimate we have for the probabilities is

Blue 845/1200

Green 305/1200

Yellow 50 /1200

We multiply by 20 to get the numerator when the denominator is twenty. This is an estimate of the number of marbles of each color;

`b=20(845/1200) \approx 14.1`

`g=20(305/1200) \approx 5.1`

`y=20(50 /1200) \approx 0.8`

Since we know there are a whole number of marbles, our best estimate of the probabilities is

Answer: Blue 14/20 Green 5/20 Yellow 1/20