CA Foundation · Quantitative Aptitude · Theoretical Distributions
If X is binomial with n = 6 and p = 1/2, which value of X has the highest probability (the mode)?
The mode is 3. For n = 6 and p = 1/2, probabilities are proportional to the binomial coefficients 1, 6, 15, 20, 15, 6, 1, which peak at x = 3. The distribution is symmetric about its mean np = 3.
- A2
- B3Correct
- C4
- D6
Explanation
Probabilities are proportional to 6Cx: 1, 6, 15, 20, 15, 6, 1 for x = 0 to 6. The largest is 20 at x = 3. Values 2 and 4 each have 15, which is lower. Also np = 3 confirms symmetry about 3.
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