Question

In a population of birds, the proportion of blue individuals is 0.4 and the proportion of males is 0.3. Assuming that colour and sex are independent of each other, the probability that a randomly sampled individual from this population is a blue male is ______ (Round off to two decimal places)

Hint:

Since colour and sex are independent, multiply the individual probabilities: P(blue) x P(male).

Answer 1

Correct Answer: 0.12

Step 1: Understanding the Question.
We are told that in a bird population, the proportion of blue individuals is 0.4, and the proportion of males is 0.3. Colour and sex are given to be independent traits. We need to find the probability that a randomly picked individual is both blue and male.

Step 2: Key Formula or Approach.
When two events are independent, the probability that both occur together is the product of their individual probabilities. If \(P(\text{blue}) \) is the probability of being blue and \(P(\text{male})\) is the probability of being male, then
\[ P(\text{blue and male}) = P(\text{blue}) \times P(\text{male}) \]
This multiplication rule only works because the question explicitly tells us colour and sex do not influence each other.

Step 3: Detailed Explanation.
We are given \(P(\text{blue}) = 0.4\) and \(P(\text{male}) = 0.3\). Since colour and sex are independent, we simply multiply these two probabilities:
\[ P(\text{blue male}) = 0.4 \times 0.3 \]
\[ P(\text{blue male}) = 0.12 \]
This value is already expressed to two decimal places, so no further rounding is needed.

Step 4: Final Answer.
The probability that a randomly sampled individual is a blue male is 0.12.
\[ \boxed{0.12} \]