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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