1. ## probability help!

can show me how to do this step by step plz!!

The table below shows the results of rolling a fair number cube 50 times during a classroom activity.

# cube data

outcome|Frequency
1 | 7
2 |12
3 |10
4 |9
5 |8
6 | 4

What is the difference between the theoretical probability of rolling a number less than 4 and the experimental results recorded in the table above?
F.8%
G.79%
H.58%
J.29%

2. Originally Posted by whatxxever_2009
can show me how to do this step by step plz!!

The table below shows the results of rolling a fair number cube 50 times during a classroom activity.

# cube data

outcome|Frequency
1 | 7
2 |12
3 |10
4 |9
5 |8
6 | 4

What is the difference between the theoretical probability of rolling a number less than 4 and the experimental results recorded in the table above?
F.8%
G.79%
H.58%
J.29%
What is the theoretical probability of rolling a number less than four?
When the problem says theoretical probability of a fair cube, you assume that every outcome is equally likely.

The theoretical probability of rolling a number less than 4 with a fair, 6 sided dice is 50% or 3/6=1/2. This is because you can roll either a 1, 2, 3, 4, 5 or 6. half of those outcomes qualify as "less than four".

To get the experimental result you have to do some more arithmetic.
7+12+10=29. There are 29, out of 50 trials, where the dice landed on less than 4. so the experimental results are that 29/50=58% of dice rolls are less than 4.

So the difference between the theoretical probability and the observed, experimental results is 58-50=8%

3. ## hi

Hi

robeuler already gave you an answer, this should be posted in the probability section though.

In general, the classical approach for estimating probabilities is through the frequentist approach used here:

Let A = "Dice showing less than 4", then

$P(A) \approx \frac{\mbox{Number of times showing less than 4}}{\mbox{Total number of trials}}$

Note the $\approx$ sign, because we would need an infinite number of trials to be certain about the true probability.

Thus, $\lim_{n\rightarrow \infty} \frac{N_{A}}{N} = P(A)$