Question

base probability review worksheet - fall 2023
a six - sided die is rolled once. 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(1)

Answer:

1. Explanation:

• Step1: Recall probability formula

The probability of an event \(E\), \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).

• 1. Roll a 5 on a die:

A standard die has 6 faces. The number of favorable outcomes of rolling a 5 is 1. The total number of outcomes is 6. So \(P(\text{roll a }5)=\frac{1}{6}\).

• 2. Roll a 1 or 6 on a die:

The number of favorable outcomes of rolling a 1 or 6 is 2. The total number of outcomes is 6. So \(P(\text{roll a }1\text{ or }6)=\frac{2}{6}=\frac{1}{3}\).

• 3. Roll an 8 on a die:

Since a standard die has values from 1 - 6, the number of favorable outcomes of rolling an 8 is 0. The total number of outcomes is 6. So \(P(\text{roll an }8) = 0\).

• 4. Roll a multiple of 3 on a die:

The multiples of 3 on a die are 3 and 6. So the number of favorable outcomes is 2. The total number of outcomes is 6. So \(P(\text{multiple of }3)=\frac{2}{6}=\frac{1}{3}\).

• 5. Roll not a 4 on a die:

The number of non - 4 outcomes is 5. The total number of outcomes is 6. So \(P(\text{not a }4)=\frac{5}{6}\).

• 6. Draw an Ace from a 52 - card deck:

A standard deck has 4 Aces. The total number of cards is 52. So \(P(\text{Ace})=\frac{4}{52}=\frac{1}{13}\).

• 7. Draw a Red card from a 52 - card deck:

There are 26 red cards (13 hearts and 13 diamonds) in a 52 - card deck. So \(P(\text{Red})=\frac{26}{52}=\frac{1}{2}\).

• 8. Draw a Diamond from a 52 - card deck:

There are 13 diamonds in a 52 - card deck. So \(P(\text{Diamond})=\frac{13}{52}=\frac{1}{4}\).

• 9. Draw a Face card from a 52 - card deck:

There are 12 face cards (4 Jacks, 4 Queens, 4 Kings) in a 52 - card deck. So \(P(\text{Face})=\frac{12}{52}=\frac{3}{13}\).

• 10. Draw a 2 or 3 from a 52 - card deck:

There are 4 twos and 4 threes. So the number of favorable outcomes is 8. The total number of outcomes is 52. So \(P(2\text{ or }3)=\frac{8}{52}=\frac{2}{13}\).

• 11. Draw a Black or Heart from a 52 - card deck:

There are 26 black cards and 13 hearts. But we need to avoid double - counting. The number of favorable outcomes is \(26 + 13=39\). So \(P(\text{Black or Heart})=\frac{39}{52}=\frac{3}{4}\).

• 12. Draw not a King from a 52 - card deck:

There are 4 Kings. So the number of non - King cards is \(52 - 4 = 48\). So \(P(\text{not a King})=\frac{48}{52}=\frac{12}{13}\).

• 13. Draw not a Face card from a 52 - card deck:

There are 12 face cards. So the number of non - face cards is \(52-12 = 40\). So \(P(\text{not a Face})=\frac{40}{52}=\frac{10}{13}\).

• 14. Draw a Blue marble from a jar with 6 red, 3 blue, and 1 white marble:

The total number of marbles is \(6 + 3+1=10\). The number of blue marbles is 3. So \(P(\text{Blue})=\frac{3}{10}\).

• 15. Draw a Red or White marble from a jar with 6 red, 3 blue, and 1 white marble:

The number of red or white marbles is \(6 + 1=7\). The total number of marbles is 10. So \(P(\text{red or white})=\frac{7}{10}\).

• 16. Draw a Green marble from a jar with 6 red, 3 blue, and 1 white marble:

The number of green marbles is 0. The total number of marbles is 10. So \(P(\text{Green}) = 0\).

• 17. Draw a non - White marble from a jar with 6 red, 3 blue, and 1 white marble:

The number of non - white marbles is \(6 + 3=9\). The total number of marbles is 10. So \(P(\text{non - white})=\frac{9}{10}\).

• 18. Draw a non - Yellow marble from a jar with 6 red, 3 blue, and 1 white marble:

Since there are no yellow marbles, the number of non - yellow marbles is \(6+3 + 1=10\). The total number of marbles is 10. So \(P(\text{non - yellow}) = 1\).

• 19. Draw a 7 from a set of numbers 1 - 20:

The number of favorable outcomes is 1. The total number of outcomes is 20. So \(P(7)=\frac{1}{20}\).

• 20. Draw a 6 or lower from a set of numbers 1 - 20:

The numbers 1, 2, 3, 4, 5, 6 are 6 numbers. The total number of outcomes is 20. So \(P(6\text{ or lower})=\frac{6}{20}=\frac{3}{10}\).

• 21. Draw an 18 or higher from a set of numbers 1 - 20:

The numbers 18, 19, 20 are 3 numbers. The total number of outcomes is 20. So \(P(18\text{ or higher})=\frac{3}{20}\).

• 22. Draw a multiple of 4 from a set of numbers 1 - 20:

The multiples of 4 are 4, 8, 12, 16, 20. So the number of favorable outcomes is 5. The total number of outcomes is 20. So \(P(\text{multiple of }4)=\frac{5}{20}=\frac{1}{4}\).

• 23. Draw a 9 or 11 from a set of numbers 1 - 20:

The number of favorable outcomes is 2. The total number of outcomes is 20. So \(P(9\text{ or }11)=\frac{2}{20}=\frac{1}{10}\).

• 24. Draw not a 15 from a set of numbers 1 - 20:

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

1. Answer:
2. \(\frac{1}{6}\)
3. \(\frac{1}{3}\)
4. \(0\)
5. \(\frac{1}{3}\)
6. \(\frac{5}{6}\)
7. \(\frac{1}{13}\)
8. \(\frac{1}{2}\)
9. \(\frac{1}{4}\)
10. \(\frac{3}{13}\)
11. \(\frac{2}{13}\)
12. \(\frac{3}{4}\)
13. \(\frac{12}{13}\)
14. \(\frac{10}{13}\)
15. \(\frac{3}{10}\)
16. \(\frac{7}{10}\)
17. \(0\)
18. \(\frac{9}{10}\)
19. \(1\)
20. \(\frac{1}{20}\)
21. \(\frac{3}{10}\)
22. \(\frac{3}{20}\)
23. \(\frac{1}{4}\)
24. \(\frac{1}{10}\)
25. \(\frac{19}{20}\)