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.

Probability of Rolling a Die

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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