Probability
What is the probability of rolling a 5 on a standard die?
1/6 ≈ 0.167 (about 16.7%)
True or False: if you flip heads 5 times in a row, tails is 'due' on the next flip.
FALSE — each flip is independent. The coin has no memory. P(tails) is still exactly 50%.
What is the median of 10, 20, 30, 40, 100?
30
Define "mean" in statistics
The average. Add up all of the values then divide by the number of values.
You flip a fair coin 1,000 times and get 523 heads. Is the coin rigged?
No — this is well within normal variation. 523/1000 = 52.3%, close to 50%. Law of Large Numbers in action.
If you just won a hand of poker, do you have a higher, lower, or the same odds of winning your next hand?
What is the mode of 1, 3, 4, 4, 5, 6, 7, 7, 7, 8, 9, 10
7, it is the most common value.
Define the "median" in statistics.
The middle value
A bag has 3 red, 5 blue, 2 green marbles. What is P(blue)?
5/10 = 1/2 = 50%
After hitting 5 shots in a row, is a basketball player more likely to hit the next?
No. Their percentage is almost identical.
A company says average employee pay is $90,000. One employee earns $800,000. What would give a better picture of typical pay?
The median.
Define probability.
How likely something is to happen, measured from 0-1 where 0 is impossible and 1 is certain
What is the probability of rolling an even number OR a number less than 3 on a standard die?
Even: {2,4,6}. Less than 3: {1,2}. Combined: {1,2,4,6} = 4 outcomes. P = 4/6 = 2/3
How many people do you need in a room for a 50% chance that two share a birthday?
23 people
Name one trick graphs use to make a small change look dramatic.
truncated y-axis (not starting at 0), missing scale, cherry-picked time range, 3D distortion, misleading labels.
What does the Law of Large Numbers state?
As the sample size grows, the sample mean converges to the expected value.