SOLUTION: a. A bag contains 8 blue marbles, 9 yellow marbles, and 10 red marbles. If a marble is drawn from the bag, and another marble is drawn, what is the probability of drawing first

Question 1182239: a. A bag contains 8 blue marbles, 9 yellow marbles, and 10 red marbles.
If a marble is drawn from the bag, and another marble is drawn, what is the probability of drawing first a blue marble and then a red marble?
_______
b. A bag contains 9 white marbles, 10 red marbles, and eight yellow marbles.
If two different marbles are drawn from the bag, what is the probability of drawing first a white marble and then a yellow marble?
_______
Round to 4 decimal places
Found 2 solutions by mathmate, ikleyn:
Answer by mathmate(429)   (Show Source): You can put this solution on YOUR website!
Given:
a. 8B, 9Y, 10R marbles.
Two marbles are drawn (with replacement)
Find P(BR)
b. 9W, 10R, 8Y marbles.
Two marbles are drawn (without replacement).
Find P(WY)

Solution, using the multiplication rule:
(a) total 27 marbles.
P(BR) = (8/27)*(10/27) =80/729 (with replacement)
= 0.1097 (to four decimal places)

(b) total 27 marbles.
P(WY) = (9/27)*(8/26) = 4/39 (without replacement)
= 0.1025 (to four decimal places)

Answer by ikleyn(52818)   (Show Source): You can put this solution on YOUR website!
.
a. A bag contains 8 blue marbles, 9 yellow marbles, and 10 red marbles.
If a marble is drawn from the bag, and another marble is drawn, what is the probability
of drawing first a blue marble and then a red marble?
_______
b. A bag contains 9 white marbles, 10 red marbles, and eight yellow marbles.
If two different marbles are drawn from the bag, what is the probability
of drawing first a white marble and then a yellow marble?
_______
Round to 4 decimal places
~~~~~~~~~~~~~~~

For problem (a), the probability is P = = 0.1140 (rounded). ANSWER For problem (b), they ask about the CONDITIONAL probability P = P(WY | the two marbles are of DIFFERENT colors). It is P = . The numerator is P(WY) = = 0.102564. The denominator is 1 - P(WW) - P(RR) - P(YY) = = 0.689459 Then the ratio P = = = 0.1488 (rounded as requested). ANSWER

Solved (correctly).

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To tutor @mathmate and to the visitor :

            The problem says NOTHING about replacement/replacements,
            which means, by DEFAULT,     NO REPLACEMENT.

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