Question

I place 10 balls into an urn; 5 are red and 5 are blue. a. If I select 3 without replacement, what is the probability all are red? b. If I select 3 with replacement, what is the probability all are red? c. I remove ? blue balls from the urn so that the probability of drawing a red ball is now 0.555. What is the value of ??

Please show the solution in detail so that i can understand

Answer 1

5 red and 5 blue balls

a) without replacement

P(all red) = 5C3/10C3 = 0.0833

b) with replacement,

P(all red) = 5/10*5/10*5/10 =0.125

c) total balls = 10-x

P(red ball) = 5/(10-x) = 0.555

10-x = 5/0.555

x = 0.990990991 ≈ 1

so, number of blue balls removed = 1