Question

A table has two drawers. The first drawer has gold coins and the second drawer has silver coins. Open a drawer randomly and take a coin. What is the probability that it is a gold coin?

Answer 1

Hint: First we will see and analyze the question and see what is asked. After that, we will write down the given information and then we will apply the formula for calculating the probability that is: \[\text{Probability of the event to happen}=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\] and then finally get the answer.

Complete step-by-step solution
Now, it is given that we have two drawers in the table out of which the first drawer has only gold coins whereas the second drawer has silver coins in it.
Now we have to find out the probability that if we draw a coin then it will be of gold, now we know that the probability of an event to happen is calculated as follows:
\[\text{Probability of event to happen}=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\]
Now, we see that only the first drawer contains gold coins so the probability of drawing a gold coin is the same as choosing the first drawer. So, the number of favorable outcomes is 1 and the total numbers of outcomes are 2 as there are two drawers.
Therefore, the Probability of drawing a gold coin is: \[\dfrac{1}{2}\]

Note: A common mistake made by a student is that they can get confused between probability and conditional probability. A conditional probability basically tells us the probability of an event given that an event has already happened. Since the probability questions are normally not very much calculative therefore explain each and every step, for better understanding.