Question

Each morning I walk to work or take a taxi to work. The probability that I walk to work is\[\dfrac{3}{5}\] , What is the probability that I take a taxi?
A. \[\dfrac{2}{5}\]
B. \[\dfrac{3}{5}\]
C. \[\dfrac{3}{7}\]
D. \[\dfrac{3}{4}\]

Answer 1

Hint: In the above problem the probability of all the events in a sample space sums up to 1. As one event is known we have to subtract the other from 1. So that we get the probability of that particular event.

Complete step-by-step answer:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. Probability can range in between 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability that a person walk to work is \[P\left( A \right)\]=\[\dfrac{3}{5}\]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
We know that \[P\left( A \right)+P\left( B \right)=1\].
The probability that a person take taxi to work is \[P\left( B \right)=1-P\left( A \right)\]
\[P\left( B \right)=1-\dfrac{3}{5}\]
\[P\left( B \right)=\dfrac{2}{5}\]
Therefore the probability that a person take taxi to work is \[P\left( B \right)=\dfrac{2}{5}\]

Note: This is a direct problem with the straight definition of probability. All the events in a sample space are equal to one. To obtain one value the other value is subtracted and obtained the solution. Take care while solving.