(a) i. In a box of 10 identical looking chocolates, 3 are Turkish Delight filled

Question

(a) i. In a box of 10 identical looking chocolates, 3 are Turkish Delight filled and the remaining 7 have camel centres. If you select 5 at random, what is the probability that the 5 selected will contain all 3 Turkish Delight sweets? ii. If, alternatively, you were to eat the sweets one at a time until you eat all the Turkish Delights, what is the probability that this happens at the 5th sweet? (b) In a population 90% are healthy and 10% have a certain disease. A test is devised for the disease which gives a correct diagnosis 95% of the time; that is it correctly detects a diseased member 95% of the time and it correctly detects a healthy member 95% of the time. Suppose a member of the population is selected at random, and the test is applied and reads positive for the disease, what is the probability that the member has in fact the disease? (a) You decide to play a game which consists of rolling a fair die.

Explanation / Answer

1 a)Given 3 Turkish Delight and 7 camel centres, total 10 chocolates

If you select 5 at random, the probability that the 5 selected will contain all 3 Turkish Delight sweets is

3C3 * 7C2 / 10C5 = 21 / 252 = 1/12 = 0.08333

b)

let's call " B " this event this is equivalent to : E1 and E2 where :
E1 = ( during the four "drawings" you suceed in drawing (and eating!!) two of the TD's) and
E2 = (the fifth is the last TD)
P(E1 ) = (3C2 ways of choosing 2TD * 7C2 ways of choosing 2 "ordinary" among 7) / 10C4
P(E1 ) = 3*21/10C4 = 63/210 = 0.3 = 3/10

situation after E1 : 6 sweets remaining and only 1 TD therefore : P(E2) = 1/6
finally : P(B) = P(E1 and E2) = 3/60 = 1/20

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