Question

Exercise 3 (SOA type). Urn I contains 10 balls: 4 red and 6 blue. Urn II contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44. What is the number of blue balls in urn II?

Answer 1

solution : 4 Red 16red n Blue 16tn balls 6 blue 그 10 balls win urn 2 each We have to draw win, 1 ball fecom becob that let calullate bability both balls are same, both ered condition to be same both Blue

P (both ball are same) = P (both ered) + P(both blue) - plist red) & P (and red) + P(1st blue) & P(and blue) 16 + 4 10 (16+ ») 10 (16+) 64 + 6n 10 *(16+) It is that given p(both balls same) 0,44 64 ton - > 0,44 10 (16+n) 64+ on - 0.44 x 108 키 64 ton (16+) (4.4x16) + 4.4n (16x404) - 64 (16*404) – 04 66 - 4.4) 6.4 ท 6-4.4 1.6 4

Since n=4 which we assumed as number of blue balls in of blue win 4 so number of blue balls in Uan 2