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### Probability - Solved Examples - Number Cube

This set of solved examples on probability deals with the simple probability problems based on a number cube.

### Solved Example 1

What is the probability that on tossing a number cube, you get the number 4?

### Solution

#### Step 1: Find the total number of possible outcomes

On tossing a number cube, you can get either one of the six faces up. Thus, there are six possible outcomes.

#### Step 2: Find the number of favorable outcomes

The number 4 is present only on one face on a number cube. Thus the number of favorable outcomes is 1.

#### Step 3: Apply the formula for theoretical probability

P(E) = "Number of favorable outcomes"/"Total number of outcomes"
P(4) = 1/6
Thus, the probability of getting a 4 on rolling a number cube is 1/6.

### Solved Example 2

What is the probability of getting an even number on rolling a number cube?

### Solution

#### Step 1: Find the total number of possible outcomes

On tossing a number cube, you can get either one of the six faces up. Thus, there are six possible outcomes.

#### Step 2: Find the number of favorable outcomes

Out of the six numbers on a number cube (1 through 6), three are even (2, 4 and 6). Thus the number of favorable outcomes is 3.

#### Step 3: Apply the formula for theoretical probability

P(E) = "Number of favorable outcomes"/"Total number of outcomes"
P(even) = 3/6 = 1/2
Thus, the probability of getting an even number on rolling a number cube is 1/2.

### Solved Example 3

What is the probability of getting a number greater than or equal to 5 on rolling a number cube?

### Solution

#### Step 1: Find the total number of possible outcomes

On tossing a number cube, you can get either one of the six faces up. Thus, there are six possible outcomes.

#### Step 2: Find the number of favorable outcomes

There are only two numbers, 5 and 6, greater than or equal to 5 on a number cube. Thus the number of favorable outcomes is 2.

#### Step 3: Apply the formula for theoretical probability

P(E) = "Number of favorable outcomes"/"Total number of outcomes"
P("greater than or equal to 5") = 2/6 = 1/3
Thus, the probability of getting a number greater than or equal to 5 on rolling a number cube is 1/3.

### Solved Example 4

What is the probability of getting a number lesser than 4 on rolling a number cube.

### Solution

#### Step 1: Find the total number of possible outcomes

On tossing a number cube, you can get either one of the six faces up. Thus, there are six possible outcomes.

#### Step 2: Find the number of favorable outcomes

There are three numbers lesser than 4 on a number cube (1, 2 and 3). Thus the number of favorable outcomes is 3.

#### Step 3: Apply the formula for theoretical probability

P(E) = "Number of favorable outcomes"/"Total number of outcomes"
P(4) = 3/6 = 1/2
Thus, the probability of getting a 4 on rolling a number cube is 1/2.

### Solved Example 5

What is the probability of getting an odd number on rolling a number cube?

### Solution

#### Step 1: Find the total number of possible outcomes

On tossing a number cube, you can get either one of the six faces up. Thus, there are six possible outcomes.

#### Step 2: Find the number of favorable outcomes

Out of 1 to 6, three numbers (1, 3 and 5) are odd on a number cube. Thus the number of favorable outcomes is three.

#### Step 3: Apply the formula for theoretical probability

P(E) = "Number of favorable outcomes"/"Total number of outcomes"
P("odd") = 3/6 = 1/2
Thus, the probability of getting an odd number on rolling a number cube is 1/2.

### Solved Example 6

What is the probability of getting a prime number on rolling a number cube?

### Solution

#### Step 1: Find the total number of possible outcomes

On tossing a number cube, you can get either one of the six faces up. Thus, there are six possible outcomes.

#### Step 2: Find the number of favorable outcomes

Out of 1 through 6, there are three prime numbers: 2, 3 and 5. Note that 1 is not a prime number. Thus, there are three favorable outcomes.

#### Step 3: Apply the formula for theoretical probability

P(E) = "Number of favorable outcomes"/"Total number of outcomes"
P("prime") = 3/6 = 1/2
Thus, the probability of getting a prime number on rolling a number cube is 1/2.

### Solved Example 7

What is the probability of getting a number greater than 7 on rolling a number cube?

### Solution

#### Step 1: Find the total number of possible outcomes

On tossing a number cube, you can get either one of the six faces up. Thus, there are six possible outcomes.

#### Step 2: Find the number of favorable outcomes

A number cube contains numbers 1 to 6. It does not have the number 7 or any number greater than 7. Thus, the number of favorable outcomes is zero.

#### Step 3: Apply the formula for theoretical probability

P(E) = "Number of favorable outcomes"/"Total number of outcomes"
P("greater than 7") = 0/6 = 0
Thus, the probability of getting a number greater than 7 on rolling a number cube is 0.

### Solved Example 8

What is the probability of getting a composite number on rolling a number cube?

### Solution

#### Step 1: Find the total number of possible outcomes

On tossing a number cube, you can get either one of the six faces up. Thus, there are six possible outcomes.

#### Step 2: Find the number of favorable outcomes

A number cube contains numbers 1 to 6, out of which the composite numbers are 4 and 6. Thus, there are two composite numbers, and hence two favorable outcomes.

#### Step 3: Apply the formula for theoretical probability

P(E) = "Number of favorable outcomes"/"Total number of outcomes"
P("composite") = 2/6 = 1/3
Thus, the probability of getting a composite number on rolling a number cube is 1/3.