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According to the manufacturer, about 26% of sour candy in a package of Sandy's Sours are grape. What is the probability that the first grape candy chosen from the bag will be, at LEAST, the third candy chosen overall?

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Answer:


Step-by-step explanation:

We assume that there are 100 sour candies, Thus-  

26 % of candy are grape implies that 26% of 100 candies are grape that is equal to 26

Now remaing candies that are not grape are 100-26 = 74

Based on the rule of multiplication:

P(A ∩ B) = P(A)/ P(B|A)  

 In the beginning, there are 26grape candies, probability of choosing first grape candy =  26C1 = 26

 After the first selection, we replace the selected grape candy so there are still 100 candies in the bag P(B|A) =  100C3 = 100 x 99 x 98 x 97!/3! X 97!

= 50 x 33 x 98

So probability =1/ 50 x 33 x 98 x 26

= 1/4204200