Question

Alex has a bag of stuffed animals containing nine bears, six lions, and three monkeys. The probability that Alex will randomly pull out a bear and then a lion is . Using this probability, determine if the event of pulling out a bear and the event of pulling out a lion was independent, dependent, both, or neither.

Answer 1

P = 0.1764

The events are dependent

Explanation:

We have a total of 9 + 6 + 3 = 18 stuffed animals.

The probability of the first animal pulled being a bear is:

P(bear) = N(bear) / N(total)

P(bear) = 9 / 18 = 0.5

Then, for the second animal, we now have only 17 stuffed animals in total.

So the probability of the second animal pulled being a lion, given the first animal was a bear, is:

P(lion | bear) = N(lion) / N(total)

P(lion | bear) = 6 / 17 = 0.3529

So the final probability is the product of these probabilities:

P = P(bear) * P(lion | bear) = 0.5 * 0.3529 = 0.1764

To find if the events are dependent or independent, let's find the probability of the first pick being a lion:

P(lion) = N(lion) / N(total)

P(lion) = 6 / 18 = 0.3333

The probability of picking a lion is different from the probability of picking a lion given we already picked a bear, so the events are dependent.