Question

basic probability review worksheet - fall 2025
a 6 - sided die is rolled one time. find:

1. p(roll a 5)
2. p(roll a 1 or 6)
3. p(odd #)
4. p(multiple of 3)
5. p(not a 4)

a card is drawn from a standard 52 - card deck. find:

1. p(ace)
2. p(red)
3. p(diamond)
4. p(face)
5. p(2 or 3)
6. p(black or heart)
7. p(not a king)
8. p(not a face)

there are 6 red, 3 blue, and 1 white marbles in a jar. find:

1. p(blue)
2. p(red or white)
3. p(green)
4. p(non - white)
5. p(non - yellow)

a random number from 1 to 20 is drawn from a hat. find:

1. p(7)
2. p(6 or lower)
3. p(18 or higher)
4. p(multiple of 4)
5. p(9 or 11)
6. p(not a 15)
7. p(21)

Explanation:

Step1: Recall probability formula

The probability formula is $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of favorable outcomes and $n(S)$ is the total number of outcomes.

Step2: Solve for P(7) (Question 19)

There is 1 favorable outcome (the number 7) and 20 total outcomes (numbers from 1 - 20). So $P(7)=\frac{1}{20}$.

Step3: Solve for P(6 or lower) (Question 20)

The favorable outcomes are 1, 2, 3, 4, 5, 6. So $n(A) = 6$ and $n(S)=20$. Then $P(6\text{ or lower})=\frac{6}{20}=\frac{3}{10}$.

Step4: Solve for P(18 or higher) (Question 21)

The favorable outcomes are 18, 19, 20. So $n(A)=3$ and $n(S) = 20$. Then $P(18\text{ or higher})=\frac{3}{20}$.

Step5: Solve for P(multiple of 4) (Question 22)

The multiples of 4 from 1 - 20 are 4, 8, 12, 16, 20. So $n(A)=5$ and $n(S)=20$. Then $P(\text{multiple of }4)=\frac{5}{20}=\frac{1}{4}$.

Step6: Solve for P(9 or 11) (Question 23)

There are 2 favorable outcomes (9 and 11) and 20 total outcomes. So $P(9\text{ or }11)=\frac{2}{20}=\frac{1}{10}$.

Step7: Solve for P(not a 15) (Question 24)

The number of non - 15 outcomes is $20 - 1=19$. So $P(\text{not a }15)=\frac{19}{20}$.

Step8: Solve for P(21) (Question 25)

There are 0 favorable outcomes (21 is not in the range 1 - 20) and 20 total outcomes. So $P(21)=0$.

Answer:

1. $\frac{1}{20}$
2. $\frac{3}{10}$
3. $\frac{3}{20}$
4. $\frac{1}{4}$
5. $\frac{1}{10}$
6. $\frac{19}{20}$
7. $0$