Question

In a large insect population, males and females are equally abundant. If a student collects four insects from this population at random, the probability that all of them are male is ............ (round off to 2 decimal places)

Hint:

When selecting items with equal probability, multiply the probability for each selection to get the overall probability.

Answer 1

Correct Answer: 0.05

Step 1: Understanding the problem.
In this problem, the probability of selecting a male insect is \( \frac{1}{2} \) because the males and females are equally abundant. The student collects four insects, so we need to calculate the probability that all four insects are male.
Step 2: Probability for each selection.
Since each insect is chosen independently, the probability of selecting a male insect for each of the four selections is: \[ P(\text{male}) = \frac{1}{2} \]
Step 3: Calculate the probability for four selections.
The probability that all four insects are male is the product of the probabilities for each selection: \[ P(\text{all male}) = \left( \frac{1}{2} \right)^4 = \frac{1}{16} = 0.0625 \]
Step 4: Conclusion.
Thus, the probability that all of them are male is \( \boxed{0.0625} \).