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
Three dice are thrown. What is the probability of getting a sum which is a perfect square?
Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?
Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?
Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?
What is the probability that all three boys sit together?
