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Question
A die is thrown 100 times. If the probability of getting an even number is `2/5` . How many times an odd number is obtained?
Solution
The total number of trials is 100. Let the number of times an even number is obtained is x.
Let A be the event of getting an even number.
The number of times A happens is x.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by P (A) and is given by
` P (A) = m/n`
Therefore, we have ` P (A) = x/100` .
But, it is given that ` P (A) = 2/5`. So, we have
`x/100 = 2/5`
⇒ 5x = 200
⇒ `x = 200/5`
⇒ x = 40
Hence an even number is obtained 40 times. Consequently, an odd number is obtained 100 - 40 = 60 times.
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