Recall that the probability of an event is the ratio of favorable outcomes to possible outcomes.
Probability=Favorable outcomes/Possible outcomes
In this exercise, we have a bag containing 9 coins.
3& nickels
& 2& pennies
3& dimes
& 1& quarterWe want to draw a coin and then, without replacing it, we draw another one. Not replacing the first coin means that the number of possible outcomes for the second draw is reduced by 1. This also means that the events are dependent, so the following formula applies.
P( Athen B)
= P( A)* P( Bafter A)
Let's take a closer look at the given compound event.
P(dime then nickel)
This means that we first need to find the probability of drawing a dime. Then we need to find the probability of drawing a nickel after the dime. Let's find each probability one at a time.
P(dime)
There are 9 coins in the bag and 3 of them are dimes.
P(A)= &P(dime)
P(A)= & 3/9=1/3
Therefore, the probability of drawing a dime is 13.
P(nickel after dime)
Now that we have already drawn one coin and did not replace it, the number of coins in the bag is reduced to 8. Because our first draw was a dime, the number of nickels did not change – there are still 3 of them.
P( BafterA)= &P( nickelafterdime)
P( BafterA)= & 3/8
Therefore, the probability of drawing a nickel after the dime is 38.
