Question

2. A die is thrown once. Find the probability of getting (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number.

Answer 1

Answer:

(1)-3, (2)-3,(3)-3

Step-by-step explanation:

when a die is thrown , the outcomes are are 1,2,3,4,5,6.

(1)- among the outcomes only 2,3,5 are prime. (2)- between 2,5 there are 3,4,5. (3)- among the outcomes of only 1,3,5 are odd. so in each case there are 3 outcomes so probability becomes 3

Answer 2

Question:-

A die is thrown. Find the probability of getting:

• A prime number  

• 2 or 4

• A multiple of 2 or 3  

• An even prime number

• A number greater than 5          

• A number lying between 2 and 6

Solution:

Given:

A dice is thrown once .

Required to find:

• Probability of getting a prime number

• Probability of getting 2 or 4

• Probability of getting a multiple of 2 or 3.

• Probability of getting an even number

• Probability of getting a number greater than five.

• Probability of lying between 2 and 6

Total number on a dice is 6 i.e., 1, 2, 3, 4, 5 and 6.

• Prime numbers on a dice are 2, 3, and 5. So, the total number of prime numbers is 3.

We know that, Probability = $\sf \dfrac{Number ~of~ favourable~ outcomes}{ Total~ number ~of~ outcomes}$

Thus, probability of getting a prime number = $\sf \dfrac{3}{6}$ = $\sf \dfrac{1}{2}$

• For getting 2 and 4, clearly the number of favourable outcomes is 2.

We know that Probability = $\sf \dfrac{Number ~of~ favourable~ outcomes}{ Total~ number ~of~ outcomes}$

Thus, the probability of getting 2 or 4 = $\sf \dfrac{2}{6}$ = $\sf \dfrac{1}{3}$

• Multiple of 2 are 3 are 2, 3, 4 and 6.

So, the number of favourable outcomes is 4

We know that, Probability = $\sf \dfrac{Number ~of~ favourable~ outcomes}{ Total~ number ~of~ outcomes}$

Thus, the probability of getting an multiple of 2 or 3 = $\sf \dfrac{4}{6}$ = $\sf \dfrac{2}{3}$

• An even prime number is 2 only.

So, the number of favourable outcomes is 1.

We know that, Probability =  $\sf \dfrac{Number ~of~ favourable~ outcomes}{ Total~ number ~of~ outcomes}$

Thus, the probability of getting an even prime number = $\sf \dfrac{1}{3}$

• A number greater than 5 is 6 only.

So, the number of favourable outcomes is 1.

We know that, Probability =  $\sf \dfrac{Number ~of~ favourable~ outcomes}{ Total~ number ~of~ outcomes}$

Thus, the probability of getting a number greater than 5 = $\sf \dfrac{1}{6}$

• Total number on a dice is 6.

Numbers lying between 2 and 6 are 3, 4 and 5

So, the total number of numbers lying between 2 and 6 is 3.

We know that, Probability = $\sf \dfrac{Number ~of~ favourable~ outcomes}{ Total~ number ~of~ outcomes}$

Thus, the probability of getting a number lying between 2 and 6 =$\sf \dfrac{3}{6}$ =$\sf \dfrac{1}{2}$

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