Question

Q1. A die is thrown Find the probability of getting (i) A Prime Number (ii) 2 or 4
(iii) A multiple of 2 or 3 (iv) A Number greater than 6

Answer 1

i. Probability of getting a prime number

Prime no’s : 1,2,3,5

Probability : 4/ 6 = 2/3 = 0.6

2. Probability of getting 2or 4

No. Of possible outcomes = 2

Probability: 2/6 = 1/3 = 0.3

3. Probability of getting a multiple of 2 or 3

No. Of possible outcomes = 3

Probability = 3/6=1/2 = 0.5

4. Probability of getting a no. Greater than 6 = 0

( only 1-6 no’s are there in a die )

Answer 2

(i) 0.5

(ii) 0.33

(iii) 0.833

(iv) 0

Step-by-step explanation:

We are given that a die is thrown and we have to find the respective probabilities;

Probability of any event =  $\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}$  

Also, Probability is never negative and does not exceed 1 which means the value of probability of any event lies between 0 and 1.

Now, throwing a dice results in 6 outcomes i.e.

Sample Space = {1, 2, 3, 4, 5, 6}

Total number of outcomes = 6

(a) Prime number are those numbers which comes only in their own table.

So, Prime number on the dice = 2, 3, 5 = Total of 3

Probability of getting a Prime number = $\frac{3}{6}$ = 0.5

(b) Probability of getting 2 or 4 = Probability of getting 2 + Probability of getting 4

                             =  $\frac{1}{6} + \frac{1}{6}$ = $\frac{1}{3}$ = 0.33

(c) Multiple of 2 = 2, 4, 6

    Multiple of 3 = 3, 6

Probability of getting a multiple of 2 or 3 = Probability of getting a multiple of 2 + Probability of getting a multiple of 3

                    =  $\frac{3}{6}+\frac{2}{6}$ = $\frac{5}{6}$ = 0.833

(d) Probability of getting a number greater than 6 = 0

Because on the dice there is no number than 6.