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Q.

Two dice are thrown at the same time. What is the probability that the product of numbers appearing on the top of the dice is less than 9?

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a

1 12  

b

11 36  

c

4 9  

d

1 4   

answer is C.

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Detailed Solution

Given that two dice are thrown at the same time.
We have to find the probability that the product of numbers appearing on the top of the dice is less than 9.
Probability of an event E is defined as:
P(E)=Number of favorable outcomesTotal number of possible outcomes
The possible outcomes, when a pair of dice is tossed together, are:
Question ImageTotal number of possible outcomes will be 36.
According to the question, favorable outcomes are obtaining the product of numbers appearing on the top of the dice less than 9.
Thus we have:
(2,4),(4,2),(1,6),(6,1),(2,3),(3,2), 1,5 , 5,1 ,(1,4),(4,1),(2,2),(1,3), (3,1),(1,2),(2,1),(1,1)  
Hence, the number of favorable outcomes = 16.
Let E   be the event of obtaining the product of numbers less than 9.
Now, the probability of obtaining that the product of numbers less than 9 is:
P(E)= 16 36 ⇒P(E)= 4 9  
Hence, the probability of obtaining the product of numbers less than 9 is 4 9  .
Therefore, option 3 is correct.
 
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