A box of 6 coins (penny, nickel, dime or quarter) worth $0.67 is shaken. What is the probability that a nickel is drawn first and then a quarter? Assume no replacement and that all coins are equally likely.
Obviously there will have to be 2 pennies.
The only way I can see to get 67 cents from 6 coins is
QQDNPP
prob(nickel, quarter) = (1/6)(2/5) = 2/30 = 1/15
or
C(1,1)C(1,1)/(C6,2) = 1/15 in combination terms
To solve this problem, we need to find the probability of drawing a nickel first and then a quarter from the box of coins.
Step 1: Determine the total number of possible outcomes.
Since there are 6 coins in the box, there are 6 possible outcomes for the first coin that is drawn.
Step 2: Find the number of favorable outcomes.
To find the probability of drawing a nickel first, we need to determine how many nickels are in the box. Since the problem does not specify, let's assume there is only 1 nickel among the 6 coins. Therefore, there is only 1 favorable outcome for the first coin drawn.
Step 3: Calculate the probability.
The probability of drawing a nickel as the first coin is the number of favorable outcomes divided by the total number of possible outcomes.
P(draw a nickel first) = favorable outcomes / total possible outcomes
P(draw a nickel first) = 1 / 6
Step 4: Repeat steps 1-3 for the second coin (quarter).
Since the first coin is not replaced, there are now 5 remaining coins in the box for the second coin to be drawn.
Number of favorable outcomes for drawing a quarter = 1 (since there is only 1 quarter)
Total possible outcomes for the second coin = 5
P(draw a quarter second) = favorable outcomes / total possible outcomes
P(draw a quarter second) = 1 / 5
Step 5: Multiply the probabilities.
Since the two events are independent (no replacement), we can multiply the probabilities of the individual events.
P(nickel first and then a quarter) = P(draw a nickel first) * P(draw a quarter second)
P(nickel first and then a quarter) = (1/6) * (1/5)
P(nickel first and then a quarter) = 1/30
Therefore, the probability of drawing a nickel first and then a quarter from the box of 6 coins is 1/30.
To find the probability of drawing a nickel first and then a quarter, we need to determine the total number of possible outcomes (sample space) and the number of favorable outcomes.
Step 1: Finding the sample space:
Since there are 6 coins in the box, the total number of possible outcomes is given by the permutation of 6 objects taken 2 at a time. This can be computed using the formula nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects taken at a time.
In this case, n = 6 and r = 2, so the sample space can be calculated as follows:
6P2 = 6! / (6-2)! = 6! / 4! = 6 * 5 = 30
Therefore, the sample space has a total of 30 possible outcomes.
Step 2: Finding the number of favorable outcomes:
To determine the number of favorable outcomes, we need to consider that a nickel is drawn first and then a quarter.
Since each coin has an equal probability of being drawn, the probability of drawing a nickel first is 1/6. After drawing the nickel, there are 5 coins left in the box, and we want to draw a quarter from these remaining 5 coins. Therefore, the probability of drawing the quarter next is 1/5.
The number of favorable outcomes can be obtained by multiplying the probabilities:
Favorable outcomes = (Probability of drawing a nickel first) * (Probability of drawing a quarter next) = (1/6) * (1/5) = 1/30
Step 3: Calculating the probability:
The probability is given by the ratio of favorable outcomes to the sample space.
Probability = Favorable outcomes / Sample space = (1/30) / (30/30) = 1/30
Therefore, the probability of drawing a nickel first and then a quarter is 1/30.