You are asked to draw THREE coins from a jar one at a time without replacement. The jar contains FIVE dimes, TEN pennies, and EIGHT quarters.
(a) What is the probability that all three coins are pennies?
prob(PPP) = (10/23)(9/22)(8/21) = 120/1771
To find the probability of drawing three pennies, we need to calculate the probability of each individual draw and multiply them together.
First, let's determine the total number of coins in the jar. There are 5 dimes, 10 pennies, and 8 quarters, making a total of 5 + 10 + 8 = 23 coins.
For the first draw, you have a total of 23 coins to choose from. Since there are 10 pennies, the probability of drawing a penny on the first try is 10/23.
After the first penny is drawn, there are now only 22 coins left in the jar, including 9 pennies. Therefore, the probability of drawing a penny on the second draw is 9/22.
For the third draw, there are now 21 coins remaining, including 8 pennies. So the probability of drawing a penny on the third draw is 8/21.
To find the probability of all three draws resulting in pennies, you multiply the probabilities of each draw together:
Probability = (10/23) * (9/22) * (8/21) ≈ 0.0537
Therefore, the probability of drawing three pennies from the jar is approximately 0.0537, or 5.37%.