CA Foundation · Quantitative Aptitude · Theoretical Distributions
A Mumbai bank finds that 20% of loan applications are rejected. Of 5 independent applications, what is the probability that at least one is rejected? (Use 0.8^5 = 0.32768.)
The probability is 0.67232. Use the complement: the chance that no application is rejected is 0.8^5 = 0.32768, so the chance of at least one rejection is 1 − 0.32768 = 0.67232. The figure 0.32768 is the probability of no rejection.
- A0.32768
- B0.67232Correct
- C0.2
- D0.99968
Explanation
P(at least one rejected) = 1 − P(none rejected) = 1 − 0.8^5 = 1 − 0.32768 = 0.67232. The value 0.32768 is the probability that none is rejected, the complement. The value 0.99968 is wrongly using 1 − 0.2^5.
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