Answer:
(a) P = 0.2821
(b) P = 0.3718
(c) P = 0.7179
(d) P = 0.6538
(e) P = 0.4231
Explanation:
There is a total of 78 coins in the bag because:
22 + 27 + 11 + 18 = 78
From those 78 coins, 22 are quarters, so the probability that Anna obtains a quarter on the first draw is:
P = 22/78 = 0.2821
Since Anna replaces each coin before the next draw, the probability for each draw is independent. Therefore, the probability that Anna obtains a penny or a dime on the second draw is calculated as:
P = (18 + 11)/78 = 0.3718
Because there are 18 pennies and 11 dimes in the bag.
In the same way, Anna will obtain at most 10 cents worth of money if she obtains a penny, a dime, or a nickel. So, the probability is equal to:
P = (27 + 11 + 18)/78 = 0.7179
The probability that Anna does not get a nickel on the fourth draw is:
P = (22 + 11 + 18)/78 = 0.6538
Finally, Anna obtains at least 10 cents if he obtains a dime or a quarter, so the probability is:
P = (22 + 11)/78 = 0.4231
Therefore, the answers are:
(a) P = 0.2821
(b) P = 0.3718
(c) P = 0.7179
(d) P = 0.6538
(e) P = 0.4231
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