A bag contains 4 red marbles and 5 blue marbles.Whats probability of randomly selecting a blue marble and then, without replacing it, selecting a red marble?

Question

I don't understand how to solve this :(

Answer 1

"a blue marble .. out of ... 4 red marbles and 5 blue marbles"    means the probability of randomly (note: this means "fair" or the probability of selecting any of the marbles is the same) selecting a blue marble is:      5/9   [success/possible]

"then, without replacing it, selecting a red marble"   means     "of" (so, we multiply) these cases, what is the probability of selecting a red marble from the 4 red and 4 blue marbles that remain?
               (5/9)*(4/8)
                 5/18

Answer 2

You can solve this in 3 parts:

 

1) What is the P(pulling a blue from the bag)?

 

There's 9 balls in the bag and 5 are blue.  So the odds are simply 5/9.

 

2) What is the P(pulling a red) given that there is now one less blue in the bag?

 

After the first pull, there are now 8 balls left in the bag: the 4 original reds and the 4 remaining blues.  So the odds of pulling a red now are 4/8 = 1/2.

 

3) What is the P(both of these events occurring)?

 

All you need to do now is multiply the first 2 ratios together to get the combined odds. (5/9)(1/2) = 5/18