Probability and Statistics Help!

Question

There are 24 popsicles in a cooler. Ten are grape. Six are orange. Eight are cherry.

If you grab 3 popsicles from the cooler, what is the probability they will be:

a) All grape

b) All the same flavour

c) Be one of each flavour

Answer 1

Hi Christopher.

 

a)  The probability that all will be grape

When picking 3 popsicles, it is without replacements unless replacement is stated.  The first pick has a chance of 10/24 that it will be grape, the second has a chance of 9/23 that it will be grape, the third, 8/24.

 

10     9     8        720         30

--- • --- • --- = ------- = -------

24   23    22     12144      506

 

 

b) all the same flavor

We've already calculated the probability that all will be grape in a) above.

The probability that all will be orange is

6       5      4         120         5

--- • --- • ---- = -------- = -----

24    23    22      12144      506

The probability that all will be cherry is

 8      7      6        336        28
--- • --- • ---- = -------- = -----
24    23    22      12144     506

 

The probability that all three will be the same color is the probability that all three will be orange or all three will be grape or all three will be cherry.

 

30/506 + 5/506 + 28/506 = 63/506

 

c)   one of each color

When picking one of each color, there are 6 ways this can be done

We can have

grape orange cherry

grape cherry orange

orange grape cherry

orange cherry grape

cherry grape orange

cherry orange grape

 

Probability (grape) =10/24

Probability (orange) = 6/24

Probability (Cherry) = 8/24

 

So the probability of any one of the above combinations is

(10/24)(6/24)(8/24) = 480/13824 = 20/576 = 5/144

 

There are 6 combinations

so the probability that you get three difference flavors is

(5/144)(6) = 30/144 = 5/24