4 pennies and 2quarters

Assuming that the coins are mixed, the table below contains the four possible outcomes of drawing two coins.

Case  1st  2nd  p₁  p₂  p=p₁p₂  value

1       c     c     ⅔ ⅗      ⅖          2c

2       c     q    ⅔ ⅖      ⁴⁄₁₅        26c

3       q     c    ⅓ ⅘      ⁴⁄₁₅        26c

4       q     q    ⅓ ⅕      ¹⁄₁₅        50c

Case 1: One penny is drawn first leaving 3c+2q (5 coins). The probability of drawing one penny from 6 coins is 4/6=⅔. The probability of drawing another penny is ⅗, because, of the remaining 5 coins, 3 are pennies. The combined probability p is ⅔×⅗=⅖, and the value of the coins drawn is two cents.

Case 2: Same p₁ as Case 1, but out of the 5 remaining coins, there are still 2 quarters, hence p₂=⅖, and p=⁴⁄₁₅, with value 26 cents.

Case 3: Two out of 6 coins are quarters, so p₁=2/6=⅓. Of the remaining 5 coins 4 are still pennies, so the probability of drawing a penny is ⅘, making p=⁴⁄₁₅ as in Case 2, with the same value.

Case 4: p₁=⅓ as in Case 3. p₂=⅕ because only one of the remaining 5 coins is a quarter, so p=¹⁄₁₅ with total value 50c.

Note that the sum of all the probabilities in the p column is 1, showing that all outcomes have been evaluated.

by Top Rated User (716k points)