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( penny then quarter)
This means that we first need to find the probability of drawing a penny. Then we need to find the probability of drawing a quarter after the penny. Let's find each probability one at a time.
P(penny)
There are 9 coins in the bag and 2 of them are pennies. Therefore, the probability of drawing a penny is 29.
P( A)=&P( penny)
P( A)=& 2/9
P(quarter after penny)
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 penny, the number of quarters did not change – there is still 1 quarter in the bag. Therefore, the probability of drawing a quarter after the penny is 18.
P( Bafter A)=&P( quarterafter penny)
P( Bafter A)=& 1/8
