00:01
In this problem, we are given information about what coins a coin first contains.
00:05
Now, a coin is drawn from the coin first and spent, then a second coin is drawn and it is spent.
00:11
We need to find the probability that the first coin drawn was a dime and the second coin drawn was a nickel.
00:16
So let us consider d to be the event that the first coin drawn was a dime, and let us consider n2 to be the event that the second coin drawn was a nickel.
00:30
Then we have been asked to determine p of d1 intersection n2.
00:35
This is because intersection represents and.
00:38
So that means we need to find the probability that the first coin is a dime and the second coin is a nickel.
00:45
Now using the multiplication rule of probability, this is equal to p of d1 times p of n2 given d1.
00:53
So consider p of d1.
00:55
This is the number of favorable outcomes divided by the total number of outcomes.
00:58
Now first of all, consider the total number of outcomes, which you write in the denominator here.
01:03
So the total number of outcomes will be the total number of coins in the purse.
01:07
So there are nine quarters, five dimes, seven pennies, and four nickels.
01:11
So the total number of coins in the purse is nine plus five plus seven plus four, and that is equal to 25.
01:18
So that's the total number of outcomes.
01:19
Next, let us consider the number of favorable outcomes, which we write in the numerator here.
01:24
Now we want to find the probability of drawing a dime.
01:27
So the number of favorable outcomes will be the number of dms, and that is given to be five...