Question

Pandora had a jar with 24 pieces of chocolate candy and 14 pierces of orange candy. She takes one piece of candy at random from the jar, puts it back, and then games a second piece of candy. Find the probability that Pandora first chooses orange candy then chocolate. Independent or Dependent?

Answer 1

84/361 or 23.27%

Independent

Explanation:

In this case the probability would be the specific amount of each divided by the total amount (that is, the sum of orange and chocolate candies).

The probability of drawing one and then the other are two different events, therefore the final probability will be the probability of each event, therefore:

`\begin{gathered} P(\text{orange) }=(14)/(24+14)=(7)/(19) \\ P(chocolate\text{) }=(24)/(24+14)=(12)/(19) \\ \text{Therefore:} \\ P(\text{orange, chocolate) }=(7)/(19)\cdot(12)/(19) \\ P(\text{orange, chocolate) }=(84)/(361)\cong23.27\text{\%} \end{gathered}`

Two events are independent if the result of the second event is not affected by the result of the first event. If A and B are independent events, the probability that both events occur is the product of the probabilities of the individual events.

In this case the events are independent because Pandora returns the first candy to the jar, which makes the events not dependent on each other.