A student goes to Subway where he sees a brand-new promotion: a $2 mystery sub w

Question

A student goes to Subway where he sees a brand-new promotion: a $2 mystery sub with 7 distinct, randomly selected toppings from a selection of 14 distinct ingredients, four of which he is allergic to. The student knows eating the sub will kill him if and only if it contains one or more of the ingredients that he is allergic to, but he also knows $2 is a good deal and so he eats the sub. a) What is the probability that the sub does not kill the student? Enter your answer as a percentage. % b) Suppose instead of 7 distinct ingredients, the sub's toppings may be repeated (i.e. selection with replacement) from the selection of 14 toppings (e.g. tomatoes may account for 3 of the 7 toppings). What is the probability that the sub does not kill the student? Enter your answer as a percentage. %

Explanation / Answer

Total number of toppings = 14

Number of toppings that wont kill the student = 14-4 = 10

Number of toppings in a sub = 7

a) P(sub does not kill the student) = 10C7/14C7 {OR (10/14)x(9/13)x(8/12)x(7/11)x(6/10)x(5/9)x(4/8)}

= 0.035 = 3.5%

b) If items are chosen with replacement, P(sub does not kill the student) = (10/14)7 = 0.095 = 9.5%

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