Question

a 6 - sided die is rolled. 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(5 or less)
3. p(even or higher)
4. p(multiple of 4)
5. p(less than 12)
6. p(5)
7. p(1)

Explanation:

1. For rolling a 6 - sided die:

• 1. \(P(\text{roll a }5)\):
• # Explanation:

Step1: Determine total outcomes

A 6 - sided die has 6 possible outcomes (\(n = 6\)).

Step2: Determine favorable outcomes

There is 1 way to roll a 5 (\(m = 1\)).
Using the probability formula \(P(A)=\frac{m}{n}\), we have \(P(\text{roll a }5)=\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)

• 2. \(P(\text{roll a }1\text{ or }6)\):
• # Explanation:

Step1: Determine total outcomes

A 6 - sided die has \(n = 6\) possible outcomes.

Step2: Determine favorable outcomes

There is 1 way to roll a 1 and 1 way to roll a 6, so \(m=1 + 1=2\).
Using the probability formula \(P(A)=\frac{m}{n}\), we get \(P(\text{roll a }1\text{ or }6)=\frac{2}{6}=\frac{1}{3}\).