Math Games

Question: Probablility and Other Math Questions?

I have a few math questions I need answered with explanations please, step by step preferably. If you can only answer one of them, that is fine too. Thanks in advance!

1) If 5 boys and 7 girls race, what is the probability of the 1st and 2nd being boys?

2) What is the probability of getting a four of a kind in a standard 5 card poker game?

3) If you add 12 to one side of a cube, add 8 to another, and decrease the third by 4, you can double the volume. What was the original length of the edge of the cube?

4) Bacteria doubles twice every day. The organism will die if the bacteria count reaches 1 billion. How many days will that take?

5) There are ten marble in a jar: 4 read and 6 blue. What is the probability of drawing a read marble the second time you draw a marble?
I can't do the problems in excel, please explain. thanks!

Answer: Let's take a second to define the probability of an event:
Number of favorable outcomes
--- divided by ---
Total number of possible outcomes

1) Assuming both boys and girls have an equal chance of winning.
(5 boys / 12 total) * (4 boys / 11 total)
= (5/12) * (4/11) = 5/33 = .151515 or 15.15%

2) What is the probablity of getting four of a kind in a standard five card poker game? (Example: 4 Aces or 4 Jacks)

(4/52) * (3/51) * (2/50) * (1/49) = 1/270725 = 0.000004

3) If you add 12 to one side of a cube, add 8 to another, and decrease the third by 4, you can double the volume. What was the original length of the edge of the cube?

The volume of a cube equals length * width * height, (right?)
Since a cube has equal sides, (length = width = height).
Let x equal the length or width or height, since they're all the same.
(x + 12) * (x + * (x - 4) = 2x^3
Solving for x, we get:
x = -4.70964 ← (not a valid solution as it is negative)
or
x = 5.28655
or
x = 15.4231

4) Bacteria doubles twice every day. The organism will die if the bacteria count reaches 1 billion. How many days will that take?

Let's use an empirical approach, (empirical = guess).
1 billion = 1,000,000,000
Starting with one bacteria:
End of 1st day → 4 bacteria
End of 2nd day → 16 bacteria
End of 3rd day → 64 bacteria
End of 4th day → 256 bacteria
End of 5th day → 1,024 bacteria
End of 6th day → 4,096 bacteria
End of 7th day → 16,384 bacteria
End of 8th day → 65,536 bacteria
End of 9th day → 262,144 bacteria
End of 10th day → 1,048,576 bacteria
End of 11th day → 4,194,304 bacteria
End of 12th day → 16,777,216 bacteria
End of 13th day → 67,108,864 bacteria
End of 14th day → 268,435,456 bacteria
End of 15th day → 1,073,741,824 bacteria

So, somewhere around the end of the 15th day,
the bacteria count reaches 1 billion.
4^x + 1 = 1,000,000,000
x = 1 + [9*ln(10) / 2*ln(2)] = 15.9487 days

5) There are ten marbles in a jar: 4 red and 6 blue.
What is the probability of drawing a read marble the second time you draw a marble.

Answer:
If the marble is replaced, then the probability is 4/10.

If the marble is not replaced, and the first marble drawn is red:
= 3/9 or .3333

If the marble is not replaced, and the first marble drawn is green:
= 4/9 or .4444

Darn tough questions, not positive I have them completely right.

Good luck in your studies,
~ Mitch ~

P.S. - You may want to post this question in the math section.

Basic Math Practices, Addition/Subtraction preview

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