Question 11 of 55beginner🔧 ApplyShort Answer2 marks

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?

Correct Answer

To determine the probability, we first calculate the total number of possible outcomes. The tank contains 5 male fish and 8 female fish. Thus, the total number of fish is calculated as 5+8=135 + 8 = 13. Since the fish is taken out at random, there are 13 equally likely outcomes.

Next, we identify the number of favourable outcomes. The event in question is taking out a male fish. There are exactly 5 male fish in the tank, so the number of favourable outcomes is 5. The probability is calculated using the formula: Probability = Number of favourable outcomesTotal number of possible outcomes\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}

Substituting the values:

P(Male fish)=513P(\text{Male fish}) = \frac{5}{13}

Therefore, the probability that the fish taken out is a male fish is 513\frac{5}{13}.

Exercise: EXERCISE 14.1 | Q: 11 | (Page Page 14)
For More Understanding

Explanation

This question is solved using the classical definition of probability found in the provided context (specifically referencing the logic in Example 7 and Example 12). The total number of outcomes represents the total population of fish (5 male + 8 female = 13). The favourable outcomes correspond specifically to the count of male fish (5). The probability is the ratio of favourable outcomes to total outcomes.

Solution Steps

  1. Step 1: Calculate the total number of fish in the tank by adding male and female fish: 5+8=135 + 8 = 13.

  2. Step 2: Identify the number of favourable outcomes (male fish) which is 5.

  3. Step 3: Apply the probability formula: P(Male fish)=Favourable outcomesTotal outcomes=513P(\text{Male fish}) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}} = \frac{5}{13}.

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