Question 347748
1. A jar has 4 red marbles, 5 green marbles and 7 blue marbles. A marble is drawn, observed and then replaced. Another marble is then drawn. Calculate:
a.) The probability that both were red marbles
The draws are independent because you replaced the 1st draw.
P(red and red) = P(red)*P(red) = (4/16)(4/16) = 1/16

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b.) The probability that there was one red and one green marble
P(red and green) = (4/16)(5/16)
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c.) The probability that neither was a blue marble
P(not blue and not blue) = (9/16)^2
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2. In a group of 100 students, 55 study Mathematical Methods and 40 study Physics. If 12 study neither subject, how many study both?
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Draw a Venn Diagram.
If 12 study neither, 88 study MM or Phy or both subjects.
With the information given, you cannot tell how many studied both.
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Cheers,
Stan H.