Question

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?

Answer 1

Hint: Here, we have to find the probability that a male fish is picked from the tank. We will find the number of favourable outcomes and the number of total outcomes. Then, we will substitute these into the formula for the probability of an event to find the required probability.

Formula Used: We will use the formula of the probability of an event, \[P\left( E \right) = \dfrac{{{\rm{Number\, of\, favourable\, outcomes}}}}{{{\rm{Number\, of\, total\, outcomes}}}}\].

Complete step-by-step answer:
First, we will find the number of total outcomes.
We know that there are 5 male fish and 8 female fish in the tank.
The total number of fish in the tank is \[5 + 8 = 13\] fish.
The fish picked at random will be one of these 13 fish.
Therefore, the total number of outcomes is 13.
Next, we will find the number of favourable outcomes.
The favourable outcomes are getting a male fish.
Thus, the favourable outcome would be picking any of the 5 male fish from the tank.
Therefore, the number of favourable outcomes is 5.
Now, we will find the probability that the fish taken out is a male fish.
The probability of an event is given by \[P\left( E \right) = \dfrac{{{\rm{Number\, of\, favourable\, outcomes}}}}{{{\rm{Number\, of\, tota\,l outcomes}}}}\].
Substituting the number of favourable outcomes as 5 and the number of total outcomes as 13, we get
\[P\left( {{\rm{Male\, fish}}} \right) = \dfrac{5}{{13}}\].
Therefore, the probability that a male fish is picked from the tank is \[\dfrac{5}{{13}}\].

Note: Probability is defined as the certainty of the occurrence of an event. It ranges from 0 to 1 where 1 will be the definite event and 0 is an impossible event. Also, the sum of all the probabilities is equal to 1.