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One dice is picked out of two unique dices and rolled. In how many ways can a person get either a prime number on the first dice or a composite number on the second dice?  
  • a)
    4
  • b)
    5
  • c)
    6
  • d)
    9
  • e)
    18
Correct answer is option 'B'. Can you explain this answer?

Answers

Approach
Step 1: Read the question carefully & understand the objective
The objective of the question is to find the number of ways in which a person can get a prime number on the first dice OR a composite number on second dice.              
There is not much information provided to us in the question itself. However, we can deduce a few things: 
  1. One of the two dices is rolled.    
  2. If a die is rolled there are three possible outcomes in the form of prime numbers i.e. 2, 3, and 5.   
  3. Similarly, there are 2 possible outcomes (4 and 6) in the form of composite numbers.    
So, let’s move on to the next step in which we’ll write the objective equation.
Step 2:  Write the objective equation enlisting all the tasks
Achievement of the objective involves two tasks:
Task 1: Getting a prime number on the first dice
Task 2: Getting a composite number on the second dice
Since the objective statement contains the word 'OR' between the two tasks, we will put an addition sign between the two tasks. The objective equation will therefore be:
(Number of ways to achieve the objective) = (Number of ways to get a prime number on the first dice) + (Number of ways to get a composite number on the second dice)
Step 3: Determine the number of ways of doing each task
Now that we have the objective equation, let’s move on to the next step to find the number of ways in which these tasks can be completed.  
  • Task 1 - Getting a prime number on the first dice
There are three prime numbers in the numbers from 1 to 6. 
Thus, there are 3 ways to do Task 1.
  • Task 2 -Getting a composite number on the second dice
There are total 2 composite numbers in the range 1-6.  
So, there are 2 ways to do Task 4. 
Step 4: Calculate the final answer
(Number of ways to achieve the objective) = 3 + 2 = 5
 
So, there are 5 different ways in which a person can get a prime number on the first dice or a composite number on the second dice.  

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ApproachStep 1: Read the question carefully understand the objectiveThe objective of the question is to find the number of ways in which a person can get a prime number on the first dice OR a composite number on second dice. There is not much information provided to us in the question itself. However, we can deduce a few things: One of the two dices is rolled. If a die is rolled there are three possible outcomes in the form of prime numbers i.e. 2, 3, and 5. Similarly, there are 2 possible outcomes (4 and 6) in the form of composite numbers.So, lets move on to the next step in which well write the objective equation.Step 2: Write the objective equation enlisting all the tasks Achievement of the objective involves two tasks:Task 1: Getting a prime number on the first diceTask 2: Getting a composite number on the second diceSince the objective statement contains the word OR between the two tasks, we will put an addition sign between the two tasks. The objective equation will therefore be:(Number of ways to achieve the objective) = (Number of ways to get a prime number on the first dice) + (Number of ways to get a composite number on the second dice)Step 3: Determine the number of ways of doing each task Now that we have the objective equation, lets move on to the next step to find the number of ways in which these tasks can be completed. Task 1 -Getting a prime number on the first diceThere are three prime numbers in the numbers from 1 to 6.Thus, there are 3 ways to do Task 1. Task 2 -Getting a composite number on the second diceThere are total 2 composite numbers in the range 1-6.So, there are 2 ways to do Task 4.Step 4: Calculate the final answer(Number of ways to achieve the objective) = 3 + 2 = 5So, there are 5 different ways in which a person can get a prime number on the first dice or a composite number on the second dice.