Jolie has 6 quarters, 6 dimes, 4 nickels, and 10 pennies in her coin purse. If two coins are drawn at random without replacement, what is the probability of drawing a quarter on the first draw and a nickel on the second draw?
Total = 6+6+4+10=26 coins
First draw:
P(Q)=one of 6 quarters from 26 coins=6/26
P(N)=one of 4 nickels from remaining 25 coins = 4/25
Probability of P(Q followed by N)=P(Q)*P(N)
To find the probability of drawing a quarter on the first draw and a nickel on the second draw, you need to determine the number of favorable outcomes (drawing a quarter first and a nickel second) and the number of total outcomes.
Let's start with the number of favorable outcomes. Since there are a total of 6 quarters, the probability of drawing a quarter on the first draw is 6 out of the total number of coins, which is 6 + 6 + 4 + 10 = 26 coins. Therefore, the number of favorable outcomes for the first draw is 6.
Now, after drawing a quarter from the purse, there are 25 coins remaining. Out of these coins, there are 4 nickels. So, the probability of drawing a nickel on the second draw is 4 out of the remaining 25 coins.
To find the total number of outcomes, you need to consider all the possible coin combinations when drawing two coins without replacement. The total number of outcomes for the first draw is 26, and after removing the quarter, the number of outcomes for the second draw is 25.
To calculate the probability of these two events happening in sequence, you need to multiply the probabilities together. Therefore, the probability of drawing a quarter on the first draw and a nickel on the second draw is:
(6/26) * (4/25) = 0.04615 (approximately)
So, the probability is approximately 0.04615 or 4.615%.
Remember, these calculations assume that the coins are drawn randomly without replacement, meaning that once a coin is drawn, it is not put back in the purse before drawing the second coin.