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Question
A coin is tossed 1000 times, if the probability of getting a tail is 3/8, how many times head is obtained?
Options
525
375
625
725
Solution
The total number of trials is 1000. Let x be the number of times a tail occurs.
Let A be the event of getting a tail.
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 /1000 `
But, it is given that `P(A) = 3/8` . So, we have
` x/1000 = 3/8`
⇒ 8x = 3000
`⇒ x = 3000/8`
⇒ x = 375
Hence a tail is obtained 375 times.
Consequently, a head is obtained 1000 - 375 = 625 times.
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