Question

A dice is thrown once. Find the probability of getting
(i) a prime number greater than 2. (ii) an even number.
(iii) a number lying between 3 and 8. (iv) an even number or a multiple of 3.​

Answer 1

Answer:

(i) P(E) = 2/6 = 1/3

(ii) P(E) = 3/6 = 1/2

(iii) P(E) = 3/6 = 1/2

(iv) This is the answer for multiple of 3 : P(E) = 2/3

     This is the answer for even no. : P(E) = 3/6 = 1/2

     This is the answer for both even no. and multiples of 3 : P(E) = 1/6

Answer 2

Answer:

1)1/3

2)1/2

3)1/2

4)3/4

Explanation:

We know dice have 6 sides ,ie, 1, 2, 3, 4, 5, 6

1)Prime numbers grater than 2 on a dice are 3, and 5.

So, the total number of prime numbers is 2.

we know :-

$\sf{}Probability =\dfrac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

$\sf{}\Rightarrow \dfrac{2}{6}$

$\sf{} \Rightarrow\dfrac{1}{3}$

Thus, probability of getting a prime number = 1/3

2)Even numbers on a dice are 2, 4 and 6.

So, the total number of even numbers is 3.

we know :-

$\sf{}Probability =\dfrac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

$\sf{}\Rightarrow \dfrac{3}{6}$

$\sf{} \Rightarrow\dfrac{1}{2}$

Thus, probability of getting a even number = 1/2

3)Number lying between 3 and 6 are 4, 5

So,total number lying between 3 and 6 is 2

we know :-

$\sf{}Probability =\dfrac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

$\sf{}\Rightarrow \dfrac{2}{6}$

$\sf{} \Rightarrow\dfrac{1}{3}$

Thus, probability of number lying between 3 and 8 = 1/3

4)Number of even number or a multiple of 3 are 2, 3, 4, 6

So,total number of even number or  multiples of  3 is 4

we know :-

$\sf{}Probability =\dfrac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

$\sf{}\Rightarrow \dfrac{4}{6}$

$\sf{}\Rightarrow \dfrac{2}{3}$

Thus, probability of number lying between 3 and 8 = 2/3

☆Know more☆

Prime number :- A number that have only 2 factors: 1 and themselves.

For example,

11 is a prime because it is divisible only by 1 and it’s number itself.

Even number :- A number which is divisible by 2.

For example,

22  is a even number because it exactly divisible by 2.

Odd number :- A number which can’t be divisible by 2.

For example,

33 is a odd number because it i not exactly divisible by 2.