Question

The probability that Vikram is late for school in the morning is 0.1. How many times would you expect Vikram to be on time in 20 mornings?

Answer 1

Hint: The probability of any event is calculated as \[P\left( A \right) = \dfrac{{favourable{\text{ outcomes}}}}{{total{\text{ possible outcomes}}}}\]. Hence, we need to calculate the probability of the event that Vikram is not late for school in the morning, we are given the probability when he is late for school, so we find the probability that he is not late for school by subtracting the given probability from 1. We calculate the number of times he will not be late for school using the above formula as the total numbers of days are known and hence the number of days on which he will arrive on time can be easily obtained.

Complete step-by-step answer:
As the probability that Vikram is late for the school in the morning is \[0.1\].
And the probability that Vikram is not late in the morning is calculated by using the below formula as,
\[P\left( X \right) + P\left( Y \right) = 1\]
Hence, \[P\left( X \right) = 0.1\]we know it and so the value of \[P\left( Y \right)\]can be calculated.
So,
\[P\left( X \right) + P\left( Y \right) = 1\], as \[P\left( X \right) = 0.1\]
And so on putting the values
\[P\left( Y \right) = 1 - P\left( X \right)\]
On simplifying, we get,
\[P\left( Y \right) = 1 - 0.1 = 0.9\]
Thus, the probability that Vikram is not late in the morning is \[0.9\].
Here favourable outcomes will be the number of days when he is not late for school, and total possible outcomes are the total number of days that are 20.
Now, substituting it in the formula of probability as \[P\left( Y \right) = \dfrac{{favourable{\text{ outcomes}}}}{{total{\text{ possible outcomes}}}}\]
Hence,
\[ \Rightarrow \]\[0.9 = \dfrac{{n\left( {nolate} \right)}}{{20}}\]
On cross multiplying, we get,
\[ \Rightarrow \]\[n(nolate) = 20 \times 0.9\]
On simplifying, we get,
\[ = 20 \times \dfrac{9}{{10}} = 18\]
Hence, for \[18\]days Vikram will not be late for the school.


Note: Remember the formula of probability that \[P\left( A \right) = \dfrac{{favourable{\text{ outcomes}}}}{{total{\text{ possible outcomes}}}}\]and also the concept that sum of all the probability is one. Use the data given in the question carefully. And calculate without any error.
Also note that probability of an event is always greater than or equal to 0 and less than equal to 1.