The following model is sometimes used to model the spread of a contagious diseas

Question

The following model is sometimes used to model the spread of a contagious disease. Suppose a box contains b black and r red marbles. A marble is drawn and c marbles of that color together with the drawn marble are replaced in the box before the next marble is drawn, so that infected persons infect while immunity to the disease may also increase. (Givens: b=7, r=5, c=2)

a. Find the probablity that the first three marbles drawn are red.

b.Show that the probablility of drawing a black on the second draw is the same as the probability of drawing a black on the first draw.

Explanation / Answer

1) P(first marble is red) = 7/12

Number of marbles before second draw = 9 red and 5 black

P(second marble is red) = 9/14

Number of marbles before third draw = 11 red and 5 black

P(third marble is red) = 11/16

P(first 3 marbles drawn are red) = (7/12)x(9/14)x(11/16) = 0.2578

2) P(black on first draw) = 5/12

P(black on second draw) = P(red on first draw and black on second draw) + P(black on both first and second draws)

= (7/12)(5/14) + (5/12)x(7/14)

= (35 + 35)/12x14

= 5/12

So, Probability of drawing a black on the second draw is the same as the probability of drawing a black on the first draw.

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