Question

1.drawing a blue marble2.drawing a marble that is not red3.drawing a red and yellow marble at once4.drawing a red or blue marble5.drawing a red marble,put it back,and then drawing a yellow marble6.drawing a yellow marble keeping it and then drawing another yellow marble7.drawing a yellow marble,given that a red marble was drawn on the first draw and not replaced

Answer 1

There are a total of 12 marbles,

4 blue marbles

3 red marbles

5 yellow marbles

First, let us find the probability of drawing a red marble, put it back, and then drawing a yellow marble.

The probability of drawing a red marble is 3/12 or 1/4.

Since we put the red marble back to the box, the total number of marbles stays the same (12 marbles)

Therefore, the probability of drawing a yellow marble is 5/12.

Now, to find the probability of of drawing a red marble, put it back, and then drawing a yellow marble, we will multiply the 2 probabilities together.

`P(R\cap Y)=P(R)* P(Y)`

Given that

P(R) = 1/4

P(Y) = 5/12

`P(R\cap Y)=(1)/(4)*(5)/(12)`
`P(R\cap Y)=(5)/(48)`

Therefore for number 5, the answer would be

`P(R\cap Y)=(5)/(48)`