there are 5 red balls, 30 black balls, and 7 pink balls in a jar. You pull one out, don't replace it, and pull another one out. Find the probability of getting two of the same color.

Question

Please show work! Working with probability problems

Answer 1

5 red 42 balls. Odds of one red = 5/42. Odds of red on the 2nd draw is 4/41

odds of two reds on two draws is 5/42(4/41) = 5/21(2/41) = 10/861

7 pink out of 42 means 7/42 = 1/6 chance of pink on one draw

chance of pick on 2nd draw is 6/41. chance of 2 pinks is (1/6)(6/41 = 1/41

30 black out of 42 means 32/40 = 16/20 chance of one black.

chance of 2nd black = 31/39. chance of two blacks = (16/20)(31/39) = (4/5)(31/39) = 124/195

chance of getting two of the same color on 2 draws without replacement is

10/861 + 1/41 + 124/195

= .0116144

+ 0,024390

+ 0.635897

= 0.67190 = about 67.2%

= slightly better than 2/3 chance of 2 of the same color

or add the 3 fractions by putting them over a common denominator, then sum their new numerators and get the exact probability of 2 of the same color.