# 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 = Frequency of 4 AppearingSum of all the Frequencies

Frequency of 4 AppearingSum of all the Frequencies

= Number of Times 4 AppearsTotal Number of Trials

Number of Times 4 AppearsTotal Number of Trials

= 28200

28200

= 750

750.

(ii) Total number of trials = 200.

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

Therefore, the probability of getting 4 or 5 = Number of Times 4 or 5 AppearsTotal Number of Trials

Number of Times 4 or 5 AppearsTotal Number of Trials

= 54200

54200

= 27100

27100.

(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 = Number of Times a Prime Number AppearsTotal Number of Trials

Number of Times a Prime Number AppearsTotal Number of Trials

= 110200

110200

= 1120

1120.