A bag contains 16 balls of the same size but different colours, one of which 5 are white, 9 are blue and 2 are red. Two balls are to be picked from the bag without replacement. Use this information to answer the following
1. Find the probabilty that both are of same colours
2.Find the probabilty that one is white and the other is blue
3.Find the probability that both are not of the same colour
4.Find the probability that the first is blue and the second is green
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Answers

2014-02-28T08:25:34+01:00
Total number of balls = 16
White balls (Nw) = 5
Blue balls (Nb) = 9
Red balls (Nr) = 2

1. If the two balls picked are of the same color, then it means;
either (first is white and second is white) or (first is blue and second is blue) or (first is red and second is red).

Substitute

× for and and + for or
(5/16
× 4/15) + (9/16 × 8/15) + (2/16 × 1/15) = 1/12 + 3/10 + 1/120 = \frac{47}{120}

2. If one is white and the other blue, it means;
first is white and second is blue
(5/16) × (9/15) = \frac{3}{16}

3. If both are not the same color, it means;
either (first is white and the second, blue) or (first is white and the second, red) or (first is blue and the second, white) or (first is blue and the second, red) or (first is red and the second, white) or (first is red and the second, blue)
= (5/16 × 9/15) + (5/16 × 2/15) + (9/16 × 5/15) + (9/16 × 2/15) + (2/16 × 5/15) + (2/16 × 9/15) = 3/16 + 1/24 + 3/16 + 3/40 + 1/24 + 3/40 = \frac{73}{120}

4. The probability of the first being blue AND second green, is zero, since there are no green balls.


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