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 (see Fig. 14.4). What is the probability that the fish taken out is a male fish?
Step-by-Step Solution
Key Concept: Probability of an event = (Number of favourable outcomes) รท (Total number of equally likely outcomes).
1. Identify the total number of fish in the tank.
$$\text{Total fish}=5\text{ (male)}+8\text{ (female)}=13.$$
2. Identify the number of favourable outcomes (choosing a male fish).
$$\text{Favourable outcomes}=5\text{ (male fish)}.$$
3. Apply the definition of probability:
$$P(\text{male fish})=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{5}{13}.$$
4. Since the fish is taken out at random, each fish is equally likely to be chosen, so the probability computed above is the required answer.
Correct Answer: 5/13