a lot contain 15 castings from a local supplier and 25 castingsfrom a supplier n

Question

a lot contain 15 castings from a local supplier and 25 castingsfrom a supplier next state. two castings are selected randomlywithout replacment , from the lot of 40. Let A be the event thatthe first casting selected is from the local supplier, and LetB be the event that the second casting selected is from the localsupplier, determine:
a) P(A) b)P(B/A) c)P(A ^ B) d) p (A U B)
suppose three castings are selected at random, withoutreplacment from the lot of 40. in addition to the definitionsof events A and B , let C denote the event that the third castingselected is from the local supplier. determine:
e) P(A ^ B ^ C) f) P(A ^ B ^ C')
thank you
a) P(A) b)P(B/A) c)P(A ^ B) d) p (A U B)
suppose three castings are selected at random, withoutreplacment from the lot of 40. in addition to the definitionsof events A and B , let C denote the event that the third castingselected is from the local supplier. determine:
e) P(A ^ B ^ C) f) P(A ^ B ^ C')
thank you

Explanation / Answer

a) a) P(A) = 15/40 =0.375

b)b) Withoutreplacement since A already picked we have only left 14 andthe total castings are 1 less (40-1 = 39) then a) P(B/A) =14/39 = 0.3589

c)  c) Text book page 42 , conditional probability,P(B/A) = P(A ^ B)/P(A) we know P(A) and we know P(B/A) .

P(A ^B) = P(B/A)* P(A) = 0.3589 * 0.375 = 0.1346

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