We are asked to calculate the probability of each of the six given events.

1. Problem Description

We are asked to calculate the probability of each of the six given events.

2. Solution Steps

1. Picking a king out of a deck of cards:

A standard deck of cards has 52 cards, and there are 4 kings (one for each suit). The probability is the number of favorable outcomes (picking a king) divided by the total number of possible outcomes (picking any card).

$P(king) = \frac{4}{52} = \frac{1}{13}$

2. Picking a diamond out of a deck of cards:

A standard deck of cards has 52 cards, and there are 13 diamonds. The probability is the number of favorable outcomes (picking a diamond) divided by the total number of possible outcomes (picking any card).

$P(diamond) = \frac{13}{52} = \frac{1}{4}$

3. Rolling a 6 on a die:

A standard die has 6 faces, numbered 1 through

6. The probability of rolling a 6 is the number of favorable outcomes (rolling a 6) divided by the total number of possible outcomes (rolling any number from 1 to 6).

$P(6) = \frac{1}{6}$

4. Rolling an odd number on a die:

A standard die has 6 faces, numbered 1 through

6. The odd numbers are 1, 3, and

5. The probability of rolling an odd number is the number of favorable outcomes (rolling 1, 3, or 5) divided by the total number of possible outcomes (rolling any number from 1 to 6).

$P(odd) = \frac{3}{6} = \frac{1}{2}$

5. Flipping heads on a coin AND rolling a 3 on a die:

The probability of flipping heads on a coin is $\frac{1}{2}$. The probability of rolling a 3 on a die is $\frac{1}{6}$. Since these events are independent, the probability of both events occurring is the product of their individual probabilities.

$P(heads \ and \ 3) = P(heads) \times P(3) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$

6. The complement of rolling a 3 on a die:

The probability of rolling a 3 on a die is $\frac{1}{6}$. The complement of an event is the probability that the event does *not* occur. The probability of the complement is 1 minus the probability of the event.

$P(not \ 3) = 1 - P(3) = 1 - \frac{1}{6} = \frac{5}{6}$

3. Final Answer

1. 1/13

2. 1/4

3. 1/6

4. 1/2

5. 1/12

6. 5/6