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- Jul 9th 2007, 06:58 AMbadboychowURGENT Probability Question
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- Jul 9th 2007, 08:16 AMrualin
When you say "he gets 2 sixes" you mean "he gets

*exactly*2 sixes?" - Jul 9th 2007, 08:19 AMbadboychow
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- Jul 9th 2007, 08:22 AMSoroban
Hello, badboychow!

You're doing great!

Quote:

A man rolls a die for 10 times. .Find the probability that:

1. he gets two 6's

2. he gets five even numbers and five odd numbers

3. he gets at least two 5's

4. he gets three 3's and three 1's

5. he gets two 6's, given that he gets two 5's

6. he doesn't get the same number consecutively

My answers are:

1. 0.2907. . .Yes!

2. 0.24609 . Correct!

3. 0.51548 . Right!

Quote:

4. Three 3's and three 1's

. . $\displaystyle {10\choose3,3,4}\left(\frac{1}{6}\right)^3\left(\f rac{1}{6}\right)^3\left(\frac{4}{6}\right)^4 \;=\;0.017781842$

Quote:

5. Two 6's, given that he gets two 5's.

Numerator: $\displaystyle P(\text{two 6's and two 5's}) \:=\:{10\choose2,2,6}\left(\frac{1}{6}\right)^2\le ft(\frac{1}{6}\right)^2\left(\frac{4}{6}\right)^6\ ;=\;0.085352843$

Denominator: $\displaystyle P(\text{two 5's}) \;=\;{10\choose2}\left(\frac{1}{6}\right)^2\left(\ frac{5}{6}\right)^8 \;=\;0.290710049$

Therefore: .$\displaystyle P(\text{two 6's }|\text{ two 5's}) \;=\;\frac{0.085352842}{0.290710049} \;=\;0.293601282$

Quote:

6. He doesn't get the same number consecutively.

The next (#2) must not match #1: .$\displaystyle \frac{5}{6}$

The next (#3) must not match #2: .$\displaystyle \frac{5}{6}$

The next (#4) must not match #3: .$\displaystyle \frac{5}{6}$

. . . and so on . . .

The last (#10) must not match #9: .$\displaystyle \frac{5}{6}$

Answer: .$\displaystyle 1 \times \left(\frac{5}{6}\right)^9 \;=\;0.193806699$

- Jul 9th 2007, 07:47 PMbadboychow
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