If a cat has 5 kittens, what is the probability that all 5 will be female?
The correct answer and explanation is:
To calculate the probability that all 5 kittens will be female, we need to assume that the probability of each kitten being female is independent of the others. In most mammals, including cats, the likelihood of a kitten being female is roughly 50% (0.5) and the probability of being male is also 50% (0.5).
Steps to calculate the probability:
- Probability of one kitten being female: As stated earlier, the probability of a kitten being female is 0.5.
- Independence assumption: The gender of one kitten does not affect the gender of another kitten, so each kitten’s gender is an independent event.
- Finding the probability for all 5 kittens: Since the events are independent, the total probability of all five kittens being female is the product of the individual probabilities. Therefore, the probability that all five kittens are female is calculated as follows:
P(all 5 female)=0.5×0.5×0.5×0.5×0.5=(0.5)5P(\text{all 5 female}) = 0.5 \times 0.5 \times 0.5 \times 0.5 \times 0.5 = (0.5)^5 P(all 5 female)=0.03125P(\text{all 5 female}) = 0.03125
Final answer:
The probability that all 5 kittens will be female is 0.03125, or 3.125%.
Explanation:
This result makes sense when considering the nature of probability in independent events. The chance of one kitten being female is 50%, and each additional kitten introduces another factor of 0.5. When you multiply these probabilities together, you get a much smaller likelihood of having all 5 kittens of the same gender. In this case, the chance of having all 5 kittens be female is only about 3.125%, which reflects how unlikely it is for such a specific gender distribution to occur by chance.