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%
What is the theoretical probability of rolling a number less than four?Originally Posted by whatxxever_2009
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%
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
$\displaystyle P(A) \approx \frac{\mbox{Number of times showing less than 4}}{\mbox{Total number of trials}} $
Note the $\displaystyle \approx $ sign, because we would need an infinite number of trials to be certain about the true probability.
Thus, $\displaystyle \lim_{n\rightarrow \infty} \frac{N_{A}}{N} = P(A) $
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