Question 1165286

One less calculation to compute this as 1-Pr(2 or fewer smokers)<br>

Probability of nonsmoker is 1-0.75 = 0.25<br>

Probability of at least 3 smokers =  1 - (probability of 2 or fewer smokers)<br>

Probability of 0 smokers: {{{ 0.25^6 = 0.0002441 }}}
Probability of 1 smoker : {{{ 0.25^5 * 0.75^1 * 6C1 = 0.0043945 }}}
Probability of 2 smokers: {{{ 0.25^4 * 0.75^2 * 6C2 = 0.0329590 }}}
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Sum is 0.037598
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Proability of at least 3 smokers = 1-0.037598 = {{{ highlight( 0.96240 ) }}}  
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You can try solving it in a direct method (pr(3)+pr(4)+pr(5)+pr(6) smokers) to prove to yourself that the answer comes out the same.<br>