Question

how do i find the odd if no replacement of pulling 2 nickels OR 2 pennies from a pool of 7 pennies, 4 nickels and 5 dimes

Answer 1

Total coins = 7 + 4 + 5 = 16.
You want P(2 nickels OR 2 pennies) with no replacement, so the two events are mutually exclusive and you can add their probabilities.

Method 1 (combinations):
- P(2 nickels) = C(4,2) / C(16,2) = 6 / 120 = 1/20.
- P(2 pennies) = C(7,2) / C(16,2) = 21 / 120 = 7/40.
- Sum = 6+21 / 120 = 27/120 = 9/40.

Method 2 (sequential):
- P(2 nickels) = (4/16) * (3/15) = 12/240 = 1/20.
- P(2 pennies) = (7/16) * (6/15) = 42/240 = 7/40.
- Sum = 1/20 + 7/40 = 9/40.

So the probability = 9/40 = 0.225 = 22.5%.
Odds in favor = 9 : 31.