What is the probability that both marbles are yellow

Question

A jar contains a total of 16 marbles 7 yellow, 4 red, 5 blue. You randomly select 2 marbles with replacement

Answer 1

There are a total of 16 marbles and 7 are yellow. The first marble selected has a 7 in 16 chance of being selected. In other words 7/16 (seven divided by sixteen), which is 0.4375. Multiply it by 100 to get percent probability of 43.75%.

That marble is then returned to the jar, and a marble is withdrawn once more at random. The probability of it being yellow is again 7 in 16.

Now the probability of getting yellow marble twice is the product of the two probabilities, or (7/16)*(7/16), which equals 0.1914, which is 19.14%.

Answer 2

Hi, Christine!

When you are replacing marbles, you reset the number of all marbles to the original conditions after each draw. With this in mind, you simply need to find the probability that a yellow is drawn once and then multiply that fraction by itself. This is because the probability of multiple events occurring in a row requires you to multiply the probability of each event.

Event one: draw a yellow.

Since there are 7 yellows out of a total of 16 marbles, the probability (desired outcomes over all possible outcomes) of drawing a yellow is 7/16.

Event two: draw a yellow.

The probability here is also 7/16 because you reset all conditions by replacing the marble after the first draw.

So, Event One x Event Two= 7/16 x 7/16 = 49/256.

Hope that helps! Feel free to reach out with any questions, etc. Thanks.

Katie