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)
Probability Calculation for Independent Events
The problem involves calculating the probability of two independent events occurring simultaneously. We are given the individual probabilities and told the events are independent.
Given Probabilities
- The probability of a bird being blue, $P(\text{Blue})$, is 0.4.
- The probability of a bird being male, $P(\text{Male})$, is 0.3.
Calculating Joint Probability
Since colour (blue) and sex (male) are stated to be independent, the probability of both events occurring (a bird being a blue male) is the product of their individual probabilities.
The formula for independent events A and B is: $P(A \text{ and } B) = P(A) \times P(B)$
Applying this to our problem:
$P(\text{Blue and Male}) = P(\text{Blue}) \times P(\text{Male})$ $P(\text{Blue and Male}) = 0.4 \times 0.3$ $P(\text{Blue and Male}) = 0.12$Final Result
The calculated probability is 0.12. Rounding this to two decimal places results in 0.12.
Important Questions from Probability
Two dice are thrown simultaneously. What is the probability of getting the same number on both the dice?
The probability of being 53 Sundays in year 2020 is-
Three dice are thrown randomly. The probability of coming 3 in at least one die is
The probability of having 53 Tuesdays in an ordinary year is:
When two dice are tossed simultaneously, the probability that the sum of the numbers appearing on both the dice is 8 will be
