A coin purse contains 10 pennies, 5 nickels, 3 dimes, and 2 quarters. Two coins are selected without the first one being replaced. Find P(quarter, then nickel).
are you on the probability chapter?
yes
If you want the prob(quarter, then nickel) in that specific order then it would be
2/20 x 5/19 = 1/38
If the order does not matter, it would be twice that, or 1/19
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To find the probability of selecting a quarter, then a nickel from the coin purse, we need to determine the total number of possible outcomes and the number of favorable outcomes.
1. Total number of possible outcomes:
Since we are selecting two coins without replacement, the total number of possible outcomes can be calculated using the concept of combinations. We need to select 2 coins from a total of 10+5+3+2 = 20 coins.
The total number of outcomes is given by the combination formula:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items being selected.
In this case, n = 20 (total coins) and r = 2 (coins being selected without replacement).
So, the total number of possible outcomes is given by:
20C2 = 20! / (2!(20-2)!) = 20! / (2!18!) = (20*19) / (2*1) = 190
Therefore, there are 190 possible outcomes when selecting two coins from the coin purse.
2. Number of favorable outcomes:
We want to select a quarter (2 choices) first, and then a nickel (5 choices) second.
Since there are 2 quarters and 5 nickels in the coin purse, the number of favorable outcomes is:
2 (quarters) * 5 (nickels) = 10
Therefore, there are 10 favorable outcomes for selecting a quarter, then a nickel.
3. Probability calculation:
Finally, the probability of selecting a quarter, then a nickel is given by:
P(quarter, then nickel) = number of favorable outcomes / total number of possible outcomes
P(quarter, then nickel) = 10 / 190
Simplifying, we get:
P(quarter, then nickel) ≈ 0.0526
So, the probability of selecting a quarter, then a nickel from the coin purse is approximately 0.0526, or 5.26%.