Your Questions About Odds Calculator Dice

Maria asks…

Probability of rolling 99, 4 times in a row on a 100 sided dice?

Say we have a random number generator that picks a number between 1 and 100. Would like to know the odds of it picking the same number 4 times in a row. I’m no good at math so I can’t figure it out. I’ve tried using rolling calculator programs but had no success. If someone could figure this out for me it’d be greatly appreciated!
What’s that in a X amount to 1 chance?

admin answers:

Odds and probability are not the same. They are related but not the same. While the probability of getting a tail on one toss of a fair coin is 1/2, the odds for getting a tail on one toss of a fair coin is 1:1 (read as one to one).

The probability of the random number generator selecting 99 on the first pick is 1/100 where 1 represents the number of 99s on the die (just one 99) and 100 represents the number of possible outcomes of tossing the die. (Die is the singular of dice –> one of a pair of dice.)

Because the die tosses are independent (the outcome of the first toss does not affect the outcome of the second toss), the probability of the second, third, and fourth consecutive tosses being a 99 are each 1/100.

Therefore the probability of 4 consective tosses of „99“ would be 1/100 time 1/100 times 1/100 times 1/100 or 1/100000000 = .00000001

George asks…

Three dice, probability problem?

If three dice are tossed and the number of dots on the top of each dice is added together, what is the probability that the sum will be odd?

I know how to do this problem, albeit slowly, on paper. But here his my actual question, is there a way to do this on the calculator? If so, please explain.

admin answers:

Dice are a, b, c

Instead of calling each die as 1,2,3,4,5,6, we can simply call it as even or odd with 50% probability.

That reduces it to 8 possible cases, each with 1/8 probability of occurring:

a even, b even, c even = total even
a even, b even, c odd = total odd
a even, b odd, c even = total odd
a odd, b even, c even = total odd
a odd, b odd, c even = total even
a odd, b even, c odd = total even
a even, b odd, c odd = total even
a odd, b odd, c odd = total odd

so 4/8 odd, and 4/8 even.

Or, a 50/50 shot of each

Daniel asks…

Theoretical Probability, Experimental Probability, Permutation and Combination? DESPERATE!!?

Hi. I understand normal probability, but I am a bit confused on the rest. For Permutation and Combination, I know I use a calculator, but which one do I do if the order matters? For example, places finished in a race? Would that be permutation or combination? Please explain to me Experimental Probability and Theoretical Probability. Here are some examples of problems:

10 people are in a race. How many different orders can all the racers finish?

There are 5 peaches, 4 plums, and 3 apples in a bowl. 2 are chosen at random and NOT replaced. What is the Probability of choosing a plum then a peach?

What is the probability of rolling a 3 or a 4 on an 8 sided dice?

Also explain odds in favor and odds against if you don’t mind..

Jack collected 40 game winning pieces. He had 5 game winning pieces. What are the odds against winning?


admin answers:

If order matters it’s a permutation.
(10 runners in a race, how many way to give gold, silver, bronze? 10 P 3)
If order doesn’t matter, it’s a combination.
(10 runners in a race, how many ways to hand out 3 medals? 10 C 3)

Theoretical Probability: what you can calculate
Experimental Probability: what actually happens.

For example, if you flip a coin 4 times, there is 1/16 chance of getting heads 4 times in a row.
If you actually flip a coin 4 times, and do *that* 160 times,
you might get 4 heads 8 or 9 or 10 or 11 or 12 or some other number of times.

The calculating 1/16 probability is Theoretical.
Actually flipping the coin and toting up the results is experimental.
If it only came heads 4 times in a row on 8 of the trials,
the experimental probability would be 1/20 (8 / 160) instead of the Theoretical (1/16).

If you did the experiment 1.6 million times instead of 160,
you’d expect the Experimental to be very close to the theoretical.

10 people in a race:
10 possibilities for 1st, 9 for 2nd, 8 for 3rd, etc:
10! = permutations

The fruit problem is also permutations since the word „then“ is in there.
Had it been „a plum AND a peach“ that would be combinations.

Probability is 4 plums / 12 fruits followed by (times) 5 peaches / 11 remaining fruits.
4 / 12 * 5 / 11 = 5/33

(If it were combinations, then you’d add the „peach, then plum“ probability,
which, not coincidentally, is the same.)

There are 8 numbers on the die, you are concerned with 2 of them: 2 / 8 = 1/4

Odds is a slightly different way of expressing probability
(and in common usage, the term „odds“ is – incorrectly – used to mean probability,
as in „What are the odds of that happening?“)

Probability is (chosen outcome) / (all outcomes).
For instance, with your die problem:
(2 chosen outcomes [3 and 4]) / (8 total [1 through 8]) = 2 / 8

There are 2 chosen outcomes and 6 others.

Odds in favor is chosen : other.
Odds against is other : chosen.

So for this problem, the odds for are 2 to 6 (or 2 : 6).
And the odds against are 6 to 2 (or 6 : 2).

Of course those can be reduced to „1 to 3“ or „3 to 1“

William asks…

Can a simple math problem illustrate God?

Is this a clear way for us to illustrate God’s miracle in life?

Take ten cards, number them 1-10, then put them in a bag. Shake the bag real well, then all you have to do is blindly pull out the cards in order, 1, then 2, then 3….all the way to 10.

A simple permutation illustrates that the odds of you doing this are 1 in 3.2 million (! 10 on your calculator).

So now understand this….the most simple of cells, a bacteria, has hundreds of key parts AND DNA string so that the cell can replicate itself PERFECTLY. Take any of key parts from the cell, it DIES immediately. Take away the DNA, it cannot reproduce itself, and it dies.

The huge mountain between life and non-life is so profound that it still humbles science today.

How could even the most simplest cell come together BLINDLY AND develop DNA?

This is just one of thousands of illustrations that clearly leave God’s fingerprint on all things; God did it my friend!

admin answers:

What are the odds of pulling all those cards out in order?

There’s your answer:: Highly unlikely.

Sharon asks…

Quick Statistics Question? (BEST ANSWER = 10 POINTS)?

How would I enter this problem:

A fair die will be rolled 12 times. What is the probability that an odd number is rolled less than 6, but more than 2 times?

Into this calculator:

I know the number of trials would = 12 and the probability of success on a single trial would = .5, but I have no idea what would be entered into the number of successes slot.

admin answers:

You have to add up all the results you get when you enter 3, 4 and 5. So enter 3 for number of successes, then add your result to what you get when you enter 4, then add that again to what you get when you enter 5 and that is your answer.

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