SOLUTION: Questions: (1) In a group of 40 people at a party, what is the probability of at least two people having the same birthday. That is those who are born on the same day of the sam

Question 461973: Questions:
(1) In a group of 40 people at a party, what is the probability of at least two people having the same birthday. That is those who are born on the same day of the same month but not necessarily the same year. Assume 365 days in a year and no twins are present at the party.
(2) Bowl Cl contains 3 red and 7 blue chips and bowl C2 contains 8 red and 2 blue chips. All chips are identical in size and shape. A die is cast and bowl Cl is selected if five or six spots show on the side that is up; otherwise, bowl C2 is selected. The selected bowl is handed to another person and one chip is taken at random. Suppose that the selected chip is red, what is the probability the selected bowl was Cl?
(3) A jelly producer makes 7 types of jelly. the producer packages gift boxes containing 4 jars of jelly, no two are of the same type. to reflect the 3 national chains through which the jelly is distributed, the producer uses 3 types of boxes. How may different gift boxes are possible?
(4)A firm uses three machines to process its work. Machine A is the most heavily used machine, machine B is used twice as often as machine C and half as often as machine A.
If machine A produces a faultless product on 80% of occasions, machine B produces a faultless product on 70% of occasions and machine Closes 10% of its products to early faults, and of the product that remains, 90% is faultless. Find the probability that a faulty product ha..'l come from machine B.
(5) A manufacturing process requires the use of a robot welder on each of the 2 assembly lines, A & B, which produce 300 & 500 units of product per day, respectively. Based on past experiences, it is believed that the welder on A produces 2% defective units, whereas the welder on B produces 5% defective units. At the end of the day, a unit was selected at random from the total production and was found to be defective. WHat is the probability that it came from line A?
Thanks in advance.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
2) Bowl Cl contains 3 red and 7 blue chips and bowl C2 contains 8 red and 2 blue chips. All chips are identical in size and shape. A die is cast and bowl Cl is selected if five or six spots show on the side that is up; otherwise, bowl C2 is selected. The selected bowl is handed to another person and one chip is taken at random. Suppose that the selected chip is red, what is the probability the selected bowl was Cl?
in three draws 3 + 8 + 8 = 19 total red chips, 2 eights because drawing that bowl is twice as likely.
3/19 the probability the selected bowl was Cl.
.
Ed
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