Melissa has 10 coins in her pocket.
2 quarters
3 dimes
4 nickel
1 penny
What is the theoretical probability of pulling a quarter out of your pocket, putting it back, then pulling out a penn?
My answer is 1/50
Also what is the theoretical probability of pulling a nickel out of your pocket, spending it, than pulling the penny out of your pocket?
My answer is 1/45
Your first answer is correct.
the second:
prob(nickel, then penny)
= (4/10)(1/9)
= 4/90
= 2/45
To calculate the theoretical probability, we need to divide the number of favorable outcomes by the total possible outcomes.
For the first scenario: pulling a quarter out of the pocket, putting it back, and then pulling out a penny.
Total possible outcomes = total number of coins in Melissa's pocket = 10
Favorable outcomes:
- The probability of pulling a quarter = number of quarters / total number of coins = 2 / 10 = 1/5
- The probability of pulling a penny = number of pennies / total number of coins = 1 / 10 = 1/10
Now, since we are putting the quarter back into the pocket, we can treat these probabilities as independent events. In other words, the outcome of the first draw does not affect the outcome of the second draw.
To calculate the probability of both events occurring, we multiply the individual probabilities together:
Probability of pulling a quarter, putting it back, and then pulling a penny = (1/5) * (1/10) = 1/50
So your answer of 1/50 is correct for the first scenario.
Now, let's move on to the second scenario: pulling a nickel out of the pocket, spending it, and then pulling out a penny.
Total possible outcomes = total number of coins in Melissa's pocket = 10
Favorable outcomes:
- The probability of pulling a nickel = number of nickels / total number of coins = 4 / 10 = 2/5
- The probability of pulling a penny = number of pennies / total number of coins = 1 / 10 = 1/10
Again, we can treat these probabilities as independent events since we are not replacing the nickel after spending it.
Probability of pulling a nickel, spending it, and then pulling a penny = (2/5) * (1/10) = 1/25
So, your answer of 1/45 for the second scenario is incorrect. The correct answer should be 1/25.
Remember, when calculating the probability, it's important to carefully consider the conditions, the total number of possible outcomes, and the number of favorable outcomes at each step.