Question

If four calves are born on a given day. What is the chance that all four will be females

• A. 1/4
• B. 1/8
• C. 1/2
• D. 1/16

Hint:

For any question asking for the probability of a specific sequence of binary outcomes (like coin tosses or male/female births), the probability is simply \( (1/2)^n \), where \( n \) is the number of events.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The sex determination of each newborn calf is an independent event with a nearly equal probability of being male or female.
The joint probability of several independent events occurring together is calculated by multiplying their individual probabilities.
Key Formula or Approach:
For \( n \) independent events, the probability of all events occurring is:
\[ P(\text{All events}) = [P(\text{Single event})]^n \]

Step 2: Detailed Explanation:
For any single birth in cattle, the probability of producing a female calf is:
\[ P(\text{Female}) = \frac{1}{2} = 0.5 \] The birth of each of the four calves is an independent biological event.
Therefore, we multiply the individual probabilities to find the chance that all four calves born on that day are female:
\[ P(\text{All 4 females}) = P(\text{Female}_1) \times P(\text{Female}_2) \times P(\text{Female}_3) \times P(\text{Female}_4) \] \[ P(\text{All 4 females}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{16} \]

Step 3: Final Answer:
The probability that all four calves will be female is 1/16.