Question

each of two urns contains green balls and red balls. One contains 8 green balls and 12 red balls. Urn two contains 5 green balls and 8 red balls. If a ball is drawn from each urn what is P (red and red)?

Answer 1

Hi there. To solve this question, we'll have to remember some properties about probabilities and events.

We know there are an amount of green and red balls in each urn and we have to determine the probability that, drawn a ball from each urn, we get red in both, that is:

`P(red\text{ and }red)`

First, notice the events (drawing a ball from each urn) are independents, since the color of the ball taken from the first urn doesn't change the probability of taking a ball from the second.

In this case, we have to multiply the probabilities of getting red in the first urn and getting red in the second urn, applying the multiplicative principle.

The probability of getting red in the first urn is the ratio between the number of favorable events to drawing red (12 red balls) and the size of the sample (20 balls in the urn), hence:

`P(red_1)=(12)/(20)=(3)/(5)`

The probability of drawing red in the second urn is analogous and is given by the ratio:

`P(red_2)=(8)/(13)`

The probability of getting red in both urns is then given by:

`P(red\text{ and }red)=P(red_1)\cdot P(red_2)=(3)/(5)\cdot(8)/(13)=(24)/(65)\approx0.37\text{ or }37\%`