SOLUTION: A bag contains 10 red marbles, 6 white marbles, and 9 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red?

Algebra ->  Probability-and-statistics -> SOLUTION: A bag contains 10 red marbles, 6 white marbles, and 9 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red?       Log On


   

Question 1206062: A bag contains 10 red marbles, 6 white marbles, and 9 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red?
The probability that all the marbles are red is
.
What is the probability that exactly two of the marbles are red?
The probability that exactly two of the marbles are red is
.
What is the probability that none of the marbles are red?
The probability of picking no red marbles is
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
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A bag contains 10 red marbles, 6 white marbles, and 9 blue marbles.
You draw 4 marbles out at random, without replacement.
.
(a) What is the probability that all the marbles are red?
.
(b) What is the probability that exactly two of the marbles are red?
.
(c) What is the probability that none of the marbles are red?
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In all, there are  10 + 6 + 9 = 25 marbles.

Of them, 10 are red;  6+9 = 15 are NOT red.


(a)  The total number of different quadruples is  C%5B25%5D%5E4 = %2825%2A24%2A23%2A22%29%2F%281%2A2%2A3%2A4%29 = 12650.

     This number goes to the denominator.

     In part (a), the number of favorable cases is C%5B10%5D%5E4 = %2810%2A9%2A8%2A7%29%2F%281%2A2%2A3%2A4%29 = 210.  

     The probability is  P = favorable%2Ftotal = 210%2F12650 = 0.0166  (rounded).    ANSWER



(b)  In part (b), the number of favorable cases is C%5B10%5D%5E2%2AC%5B15%5D%5E2 = %28%2810%2A9%29%2F%281%2A2%29%29%2A%28%2815%2A14%29%2F%281%2A2%29%29 = 45*105 = 4725.  

     The probability is  P = favorable%2Ftotal = 4725%2F12650 = 0.3735  (rounded).    ANSWER


(c)  P = %2815%2F25%29%2A%2814%2F24%29%2A%2813%2F23%29%2A%2812%2F22%29 = 0.1079 (rounded).    ANSWER

Solved in full.

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