Question

An urn contains 5 red 2 green 3 blue and 7 yellow marbles. a marble is chosen at random from the urn. after replacing it, a second marble is chosen. what is the probability of chosing a red and then a yellow roll?

Answer 1

Given:

red - 5

green - 2

blue - 3

yellow - 7

total number of marbles = 17

Find: probability of rolling a red, then a yellow.

Solution:

Let's solve first the probability of rolling a red.

Since there are 17 marbles and there are 5 red marbles, then the probability of rolling a red is 5/17.

Now, since a replacement was provided, this means, there will still be 17 marbles in the urn. Out of the 17 marbles, there are 7 yellow marbles. Hence, the probability of rolling a yellow on the second roll is 7/17.

So, to get the probability of rolling a red AND then a yellow, multiply the two probabilities above.

`\begin{gathered} =P(red)* P(yellow) \\ =(5)/(17)*(7)/(17) \\ =(35)/(289)or0.121107\text{ }or\text{ }12.11\% \end{gathered}`

Answer:

The probability of chosing a red and then a yellow roll is 35/289 or 12.11% approximately.