Question

A bag contains 4 b l u e marbles, 3 w h i t e marbles, and 10 r e d marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a b l u e marble and then a r e d marble?

Answer 1

40/289

Explanation:

We can see these two events are independent as Regina replaced marble after drawing one marble.

We can find possible outcomes by adding number of blue, red and yellow marbles.

possible outcomes= 4+3+10= 17

Let us find probability of getting a blue marble on first draw.

`P( blue\ marble)= (4)/(4+3+10) = (4)/(17)`

Now we will find probability of getting red marble.

`P(red/marble)= (10)/(17)`

We can find probability of getting a blue marble and then red marble by multiplying both probabilities.

`P(\text{ Blue then red})=(4)/(17)* (10)/(17) =(40)/(289)`