Question

• probability •

a shortcut to finding out the total number of combinations of a set of events is to multiply the number of possibilities for each event together. this is called the fundamental counting principle.
example: if 1 of the 4 cards is picked at random and a die is rolled once, what is the total number of combinations of the cards and die?
we know that there are 4 different suits (heart, club, diamond, and spade) and 6 different die faces (1, 2, 3, 4, 5, and 6).
to find out the total number of combinations of drawing a card and rolling a die, we simply multiply 4 by 6.
4×6 = 24
number of suits number of die faces number of combinations
try these: find the total number of combinations using the fundamental counting principle.

1. rolling a die and flipping a coin ____
2. rolling 2 dice ____
3. choosing a letter from the alphabet and flipping a coin ____
4. flipping a coin 4 times ____
5. rolling a die 3 times ____

Explanation:

Step1: Identify possibilities for each event in (1)

A die has 6 faces and a coin has 2 sides.

Step2: Apply fundamental counting principle for (1)

$6\times2 = 12$

Step3: Identify possibilities for each event in (2)

Each die has 6 faces. For 2 dice, we consider them as two - independent events.

Step4: Apply fundamental counting principle for (2)

$6\times6=36$

Step5: Identify possibilities for each event in (3)

There are 26 letters in the alphabet and a coin has 2 sides.

Step6: Apply fundamental counting principle for (3)

$26\times2 = 52$

Step7: Identify possibilities for each event in (4)

Each coin - flip has 2 possibilities. For 4 coin - flips, they are independent events.

Step8: Apply fundamental counting principle for (4)

$2\times2\times2\times2=2^4 = 16$

Step9: Identify possibilities for each event in (5)

Each die - roll has 6 possibilities. For 3 die - rolls, they are independent events.

Step10: Apply fundamental counting principle for (5)

$6\times6\times6=6^3 = 216$

Answer:

1. 12
2. 36
3. 52
4. 16
5. 216