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Maya is playing a game at the carnival. There are 25 balloons, and if she pops one with a dart, she wins the stuffed animal attached to that balloon. The balloons and their attached stuffed animals are shown below:
Row 1: bear cat cat dog elephant.
Row 2: cat pig dog bear cat.
Row 3: rabbit bear rabbit pig elephant.
Row 4: cat dog rabbit cat bear.
Row 5: dog elephant pig cat rabbit.
Assume that every throw pops a balloon and each balloon has an equal chance of being popped.
(a) Which stuffed animal is Maya most likely to win?
(b) Which stuffed animal is Maya least likely to win?
(c) Which stuffed animals are equally likely to be won by Maya?
(d) Is it likely that Maya will win an elephant?
To answer these questions, we should first tally the number of each stuffed animal:
Type of Animal | Number
—————|——-
bear | 4
cat | 7
dog | 4
elephant | 3
pig | 3
rabbit | 4
We should also note that there are 25 balloons in total.
(a) Since it is equally likely to pop any balloon, and since there are more balloons with a cat than any other animal, a cat is the most likely stuffed animal to be won.
(b) Since it is equally likely to pop any balloon, and since there are fewer balloons with elephants or pigs than any other animal, an elephant or a pig is the least likely stuffed animal to be won.
(c) Since there are the same number of balloons that contain a bear, a dog, and a rabbit, it is equally likely to win any of these three animals.
(d) Since there are 3 balloons that contain an elephant and 22 balloons that do not contain an elephant, it is not likely that Maya will win an elephant. The probability of winning an elephant is 3/25 or 12%, which is relatively low.
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