Questions: A die is rolled. Find the probability of the given event. (a) The number showing is a 4 ; The probability is : (b) The number showing is an even number; The probability is : (c) The number showing is greater than 4 ; The probability is :

A die is rolled. Find the probability of the given event.
(a) The number showing is a 4 ;

The probability is :
(b) The number showing is an even number;

The probability is :
(c) The number showing is greater than 4 ;

The probability is :

Transcript text: A die is rolled. Find the probability of the given event. (a) The number showing is a 4 ; The probability is : $\square$ (b) The number showing is an even number; The probability is : $\square$ (c) The number showing is greater than 4 ; The probability is : $\square$

Solution

Solution Steps

Step 1: Determine the total number of possible outcomes

A standard die has 6 faces, numbered from 1 to 6. Therefore, the total number of possible outcomes when rolling the die is $ 6 $.

Step 2: Calculate the probability of rolling a 4

There is only 1 favorable outcome for rolling a 4. The probability $ P $ of rolling a 4 is given by: \[ P(\text{4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{6} \]

Step 3: Calculate the probability of rolling an even number

The even numbers on a die are 2, 4, and 6. There are 3 favorable outcomes. The probability $ P $ of rolling an even number is: \[ P(\text{Even}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{6} = \frac{1}{2} \]

Step 4: Calculate the probability of rolling a number greater than 4

The numbers greater than 4 on a die are 5 and 6. There are 2 favorable outcomes. The probability $ P $ of rolling a number greater than 4 is: \[ P(\text{Greater than 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{6} = \frac{1}{3} \]