G(1 point) Two marbles are drawn randomly one after the other without replacement from a jar that contains 3 red marbles, 3 white marbles, and 6 yellow marbles. Find the probability of the following events, accurate to 4 decimal places. (a) A red marble is drawn first followed by a white marble. The probability is : (b) A white marble is drawn first followed by a white marble. The probability is : (c) A yellow marble is not drawn at all. The probability is :

(a)

(b)

(c)  

Step-by-step explanation:

We are given that Two marbles are drawn randomly one after the other without replacement from a jar that contains 3 red marbles, 3 white marbles, and 6 yellow marbles.

So, total number of marbles = 3 + 3 + 6 = 12 marbles

(a) Probability that a red marble is drawn first followed by a white marble is given by;

First P(drawing red marble) =

Now, since one red marble has been drawn so now the total marbles remaining will be 12 - 1 = 11 marbles and from this white marble will be drawn.

P(drawing white marble) =

Therefore, Probability that a red marble is drawn first followed by a white marble = = .

(b) Probability that a white marble is drawn first followed by a white marble is given by;

P(drawing first white marble) =

Now, the white marbles remaining are 3 - 1 = 2 marbles and total number of marbles are 12 - 1 = 11 marbles.

So, P(drawing another white marble) =

Therefore, Probability that a white marble is drawn first followed by a white marble = = .

(c) Probability that a yellow marble is not drawn at all is given by;

Now both the marbles will be drawn from red and white marbles i.e. 6   marbles and total marbles will be 12

So, probability that a yellow marble is not drawn at all = =

                        = = = = .

37

step-by-step explanation: