The probability that you win at most once when the chances of winning are 0.2, if you play the lottery five times and outcomes are independent is 0.7373
Thus the answer is (d) 0.7373
This is a case of Binomial expansion. Here the chances of winning is the probability of successful trial, i.e. 0.2 and thus the probability of failure is (1-0.2) = 0.8. Total number of trials is 5.
Given probability that you win at most once, that is it includes probability of winning once and probability of not winning. So number of successful trial is 1 and 0 in case 1 and case 2.
Probability = 5C0×0.2^{0}×0.8^{5-0} + 5C1×0.2^{1}×0.8^{5-1}
= 1×1×0.32768 + 5×0.2×0.4096
= 0.73728
≅ 0.7373
To know more about Binomial expansion
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