CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
A binomial random variable has n = 10 trials and a success probability of 0.30 on each independent trial. The probability of exactly 2 successes is closest to:
The probability is about 0.233. Using the binomial formula, C(10,2) equals 45, multiplied by 0.3 squared (0.09) and 0.7 to the eighth power (0.0576), which gives roughly 0.2335.
- A0.121
- B0.233Correct
- C0.267
Explanation
P(X=2) = C(10,2)(0.3)^2(0.7)^8 = 45 × 0.09 × 0.05765 = 0.2335. The value 0.121 is P(X=1)... actually P(X=1)=0.121; 0.267 is P(X=3). Both use the wrong number of successes.
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