March 11, 2021

Chapters

In this article, we will see how to solve different types of probability word problems. But before proceeding to examples, let us define the probability first.

## What is Probability?

Probability can be defined as:

The possibility of the occurrence of a random event

The formula for calculating the probability is given below:

The probability of a certain event is 1 and an impossible event is 0. The probability is always positive.

## Example 1

There are 50 cookies in a box. Out of 50 cookies, 15 are chocolate-flavored, 20 are caramel-flavored, and the remaining are salted cookies. What is the probability of picking up:

a) a chocolate cookie randomly

b) a chocolate or caramel-flavored cookie

c) a chocolate and salted cookie

### Solution

### Part a

Number of chocolate-flavored cookies in a box = 15

Total number of cookies in a box = 50

Probability of picking up chocolate-flavored cookie =

### Part b

Number of chocolate-flavored cookies in a box = 15

Number of caramel-flavored cookies in a box = 20

Total number of cookies in a box = 50

Probability of picking up chocolate-flavored cookie = P(A) =

Probability of picking up a caramel-flavored cookie = P(B) =

Probability of picking up a chocolate or caramel cookie = P(A) U P(B)

=

=

### Part c

Probability of picking up a chocolate cookie = P(A) =

Probability of picking up a caramel= P(B) =

Probability of picking up a chocolate or caramel cookie=

Both events are mutually exclusive, so the probability of picking up a chocolate and caramel cookie is 0.

## Example 2

### Solution

### Part a

### Part b

### Part c

## Example 3

### Solution

## Example 4

### Solution

## Example 5

In an area, 47% of the families own a car and a bike. 53% of the families own a car. What is the probability of a family owning a bike given that it already owns a car?

**Solution**

Percentage of the families who own both car and a bike = 47%

Probability of families owning a car and a bike= P(C and B) = 0.47

Percentage of families owning a car = 53%

The probability of families owning a car only = P(C) = 0.53

## Example 5

Two dice are rolled simultaneously. What is the probability that the sum is:

a) less than 10

b) equal to 4

c) greater than 10

### Solution

### Part a

Total number of outcomes = 6 x 6 = 36

Sample space = S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6), (2,1),(2,2),(2,3),(2,4),(2,5),(2,6), (3,1),(3,2),(3,3),(3,4),(3,5),(3,6), (4,1),(4,2), (4,3),(4,4),(4,5),(4,6), (5,1),(5,2),(5,3),(5,4),(5,5),(5,6), (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) }

### Part b

### Part c

## Example 6

What is the probability of selecting two prime number cards from the deck of 52 cards?

### Solution

First, we will evaluate the types of cards present in each deck. A deck of 52 cards has the following attributes:

- There are four suits in a deck. Each suit has 13 cards
- Two of the four suits are black cards and two are red.
- The 13 cards in each suit include a king, a queen, a jack, ace, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

In each suit, there are four prime numbers 2, 3, 5, and 7. Hence, in four suits, there will be 16 cards

Number of prime number cards in a deck = 16

Total number of cards in a deck = 52

The probability of selecting a prime number card from a deck =

Now, we will calculate the probability of picking up the second prime number card from the deck.

Number of prime number cards left in a deck = 15

Total number of cards left in a deck = 51

The probability of drawing a prime number card, given a prime number card has already been drawn =

In this problem, we need to compute the probability of picking up two prime number cards, therefore we will multiply the probabilities we have calculated above:

=

## Example 7

### Solution

### Part a

### Part b

### Part c