Question

4. An urn contains 5 blue balls, 3 green balls, and 7 white balls. (a) A ball is selected from the urn. What are the odds the ball is green? (2 Two balls are selected without replacement. What are the odds the balls are blue and green? (c) Two balls are selected without replacement. What are the odds at least one is blue or at least one is green? (d) Two balls are selected without replacement. What are the odds the both balls are blue or both are green?

Answer 1

(a). The total number of balls = 5 + 3 + 7 = 15

P(G) = 15 = 5 3

(b). Two balls can be blue and green in two ways because the first ball drawn is not replaced, therefore the order of the balls matter.

Case 1: First ball is blue, second is green

P(B then G) =-× 15 1414

Case 2: First ball is green, second is blue

P(G then B) 15 1414

Total probability is given by

Pl B and G) = 14 14 7

(c). P( At least one if blue or at least one is green) = 1 - P(Both are white)

P(W,W) = 15 14 5

P(required)-1--=

(d). Case 1: Both are blue

PlB.B) _ 15 × 11-21

Case 2 : Both are green

15 14 35

2 13 P(required) 35105 21 35105