Probability and Statistics — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The probability of flipping heads on a fair coin is 1/3.
Corrected: The probability of flipping heads on a fair coin is 1/2.
Two equally likely outcomes give one favorable over two total, which is one half.
2. Fix the sentence:
Rolling a 7 on a standard six-sided die is likely.
Corrected: Rolling a 7 on a standard six-sided die is impossible.
A standard die only shows 1 through 6, so 7 can never appear at all.
3. Fix the sentence:
If a bag has only red marbles, drawing red is unlikely.
Corrected: If a bag has only red marbles, drawing red is certain.
When every outcome is the same color, that color must always happen.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. An event that will definitely happen is called certain.
Certain events have probability one because they always occur in every trial.
2. The probability of flipping tails on a fair coin is 1/2.
One tail outcome divided by two equal coin sides equals one half.
3. Rolling a 4 on a standard six-sided die has probability 1/6.
Each of the six die faces is equally likely, so one over six.
4. An event that cannot happen is called impossible.
Impossible events have probability zero because they never occur in any trial.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Describe the chance of pulling a blue marble from a bag with 1 blue and 9 red marbles.
Sample answer: The chance is unlikely because only 1 out of 10 marbles is blue, giving probability 1/10.
When favorable outcomes are much smaller than total, the event is unlikely.
2. Explain why rolling a number less than 7 on a standard die is certain.
Sample answer: Every face on a die shows 1, 2, 3, 4, 5, or 6, and all are less than 7, so the event always happens.
When every outcome satisfies the event, probability equals one and it is certain.