# Probability of Rolling a Die

We will solve different type of problems on probability of rolling a die.

1. A die is thrown 200 times and the numbers shown on it are recorded as given below:

If the die is thrown at random, what is the probability of getting a

(i) 4

(ii) 4 or 5

(iii) Prime number

Solution:

(i) Total number of trials = 200.

Number of times 4 appears = 28.

Therefore, the probability of getting 4 = $$\frac{\textrm{Frequency of 4 Appearing}}{\textrm{Sum of all the Frequencies}}$$

= $$\frac{\textrm{Number of Times 4 Appears}}{\textrm{Total Number of Trials}}$$

= $$\frac{28}{200}$$

= $$\frac{7}{50}$$.

(ii) Total number of trials = 200.

Number of times 4 or 5 appears = 28 + 26 = 54.

Therefore, the probability of getting 4 or 5 = $$\frac{\textrm{Number of Times 4 or 5 Appears}}{\textrm{Total Number of Trials}}$$

= $$\frac{54}{200}$$

= $$\frac{27}{100}$$.

(iii) Total number of trials = 200.

Number of times a prime number appears = 48 + 36 + 26 = 110.

[Since 2, 3 and 5 are prime numbers and they appear 48, 36 and 26 times respectively).

Therefore, the probability of getting

a prime number = $$\frac{\textrm{Number of Times a Prime Number Appears}}{\textrm{Total Number of Trials}}$$

= $$\frac{110}{200}$$

= $$\frac{11}{20}$$.

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