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5 boxes, each containing 12 white balls











































A man has a 5 boxes, each containing 12 white balls and 8 black balls. What are the odds of the man pulling a white ball from
A) 1 box
B) 3 consecutive boxes
C) 5 consecutive boxes

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Aug 20, 2011
Probability
by: Staff


The question:

A man has 5 boxes, each containing 12 white balls and 8 black balls. What are the odds of the man pulling a white ball from

A) 1 box
B) 3 consecutive boxes
C) 5 consecutive boxes

The answer:

Your question is similar to calculating the chance of flipping a coin and getting a head 1 time, 3 times in a row, or 5 times in a row.

When flipping a coin, the theoretical probability of getting a head is ½ for each toss. One toss does not affect the probability for the next toss.

If you are tossing a coin, the theoretical probability of always getting a head is:

1 toss (1 head): P(H) = ½

3 tosses (3 heads in a row): P(H) = ½ * ½ * ½ = 1/8

5 tosses (5 heads in a row): P(H) = ½ * ½ * ½ * ½ * ½ = 1/32


When pulling a white ball from one of the boxes in your question, the theoretical probably of retrieving a white ball is calculated exactly the same way.

However, the theoretical probability of getting a white ball from a single box is not ½.

Each time you randomly retrieve a ball from one of your boxes, the chance of picking a white ball is:

P(w) = (12 white balls)/(20 balls, total)

P(w) = (12)/(20)

P(w) = 3/5, or 0.6


The theoretical probability of always getting a white ball is:

1 box (1 white ball):

P(w) = 3/5 = 0.6

3 boxes (3 white balls in a row):

P(www) = 3/5 * 3/5 * 3/5 = 27/125 = 0.216

5 boxes (5 white balls in a row):

P(wwwww) = 3/5 * 3/5 * 3/5 * 3/5 * 3/5 = 243/3125 = 0.07776

These types of probability are often represented graphically on a tree diagram.

(1) Click the following link to VIEW the tree diagram; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/tree-diag-select-white-ball-2011-08-20.png





The final answer is:

The theoretical probability of always getting a white ball is:

1 box (1 white ball): P(w) = 3/5 = 0.6

3 boxes (3 white balls in a row): P(www) = 27/125 = 0.216

5 boxes (5 white balls in a row): P(wwwww) = 243/3125 = 0.07776




Thanks for writing.

Staff
www.solving-math-problems.com


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