Question

a) Two balls are drawn without replacement from an urn containing 12 balls, of which 7 are white and 5 are black. Find the probability that: (i) Both balls will be white (ii) Both balls will be the same color (iii) At least one of the balls will be white

b) Repeat part (a) but with the balls drawn with replacement

Answer 1

Total number of balls = 12

Number of white balls = 7

Number of black balls = 5

(a) Without replacement,

(i) P(both will be white) = 7/12 x 6/11

= 0.3182

(ii) P(both will be same color) = P(both white) + P(both black)

= 0.3182 + 5/12 x 4/11

= 0.3182 + 0.1515

= 0.4697

(iii) P(at least one white) = 1 - P(both black)

= 1 - 0.1515

= 0.8485

(b) With replacement,

(i) P(both will be white) = 7/12 x 7/12

= 0.3403

(ii) P(both will be same color) = P(both white) + P(both black)

= 0.3403 + 5/12 x 5/12

= 0.3403 + 0.1736

= 0.5139

(iii) P(at least one white) = 1 - P(both black)

= 1 - 0.1736

= 0.8264