Answer
Verified
494.1k+ views
Hint: First find out the numbers which are divisible by 3.
Then divide the number of favourable outcomes by the total number of outcomes to get the required probability.
Complete step by step solution:
Probability means possibility. Probability is a measure of the likelihood of an event to occur. The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Here in the given question we have a set $\left\{ 2,4,6,8,10,12,14,16,18 \right\}$
The set has 9 elements.
So if we select a number from this set at random we can get at most 9 different numbers.
So, here the total number of outcomes are 9.
Now we have to find out the total number of favourable outcomes.
Here, our favourable outcomes will be those numbers which are divisible by 3.
Divisible by 3 means, if we divide that number by 3 the remainder should be 0.
Now let us check which numbers are divisible by 3 here.
We know that, 2 is not divisible by 3.
4 is not divisible by 3, as the remainder is 1.
6 is divisible by 3, as the remainder is 0.
8 is not divisible by 3, as the remainder is 2.
10 is not divisible by 3, as the remainder is 1.
12 is divisible by 3, as the remainder is 0.
14 is not divisible by 3, as the remainder is 2.
16 is not divisible by 3, as the remainder is 1.
18 is divisible by 3, as the remainder is 0.
Therefore, there are 3 numbers which are divisible by 3.
Those are 6, 12, 18.
So, our total number of favourable outcomes are 3.
So, the probability of selecting the numbers which are divisible by 3 is:
$\dfrac{3}{9}=\dfrac{1}{3}$
Hence, option (a) is correct.
Note: We generally make mistakes while counting the total number of favourable cases. We have to read the question very carefully to understand the favourable cases.
Then divide the number of favourable outcomes by the total number of outcomes to get the required probability.
Complete step by step solution:
Probability means possibility. Probability is a measure of the likelihood of an event to occur. The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Here in the given question we have a set $\left\{ 2,4,6,8,10,12,14,16,18 \right\}$
The set has 9 elements.
So if we select a number from this set at random we can get at most 9 different numbers.
So, here the total number of outcomes are 9.
Now we have to find out the total number of favourable outcomes.
Here, our favourable outcomes will be those numbers which are divisible by 3.
Divisible by 3 means, if we divide that number by 3 the remainder should be 0.
Now let us check which numbers are divisible by 3 here.
We know that, 2 is not divisible by 3.
4 is not divisible by 3, as the remainder is 1.
6 is divisible by 3, as the remainder is 0.
8 is not divisible by 3, as the remainder is 2.
10 is not divisible by 3, as the remainder is 1.
12 is divisible by 3, as the remainder is 0.
14 is not divisible by 3, as the remainder is 2.
16 is not divisible by 3, as the remainder is 1.
18 is divisible by 3, as the remainder is 0.
Therefore, there are 3 numbers which are divisible by 3.
Those are 6, 12, 18.
So, our total number of favourable outcomes are 3.
So, the probability of selecting the numbers which are divisible by 3 is:
$\dfrac{3}{9}=\dfrac{1}{3}$
Hence, option (a) is correct.
Note: We generally make mistakes while counting the total number of favourable cases. We have to read the question very carefully to understand the favourable cases.
Recently Updated Pages
Identify the feminine gender noun from the given sentence class 10 english CBSE
Your club organized a blood donation camp in your city class 10 english CBSE
Choose the correct meaning of the idiomphrase from class 10 english CBSE
Identify the neuter gender noun from the given sentence class 10 english CBSE
Choose the word which best expresses the meaning of class 10 english CBSE
Choose the word which is closest to the opposite in class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
10 examples of friction in our daily life
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is pollution? How many types of pollution? Define it