What is the probability that the second apple you pick is red?

Question

nvolving the selection of two apples from a bag of red and yellow apples without replacement. Assume that the bag has a total of 10 apples: 6 red and 4 yellow.
(1) What is the probability that the second apple you pick is red?

(2) What is the probability that you pick at least one red apple?

Answer 1

Hi Katie,

 

Remember, probability always boils down to:

 

     desired outcome    

total possible outcomes

 

So, we want our second apple to be red.

There are 2 ways this can happen independently:

Either our first apple AND our second apple are both red . . .

OR the first apple is yellow, and the second is red.

 

First, the chances that both are red:

 

  6   *   5   =   30   =   1 

 10       9        90        3

 

(You multiply because the probability of the second selection depends on the first.)

Next, the chances that only the second is red:

 

  4   *   6   =   24   =   4  

 10       9        90        15

 

To find the chance that one OR the other happens, you ADD:

 

  1   +   4   =   5   +   4   =   9   =   3 

  3       15       15     15       15       5

 

 

To answer your second question, remember this handy rule:

 

To find the probability that "at least one" thing happens,

find the probability of "none" happening, and subtract that from 1.

 

So, what are the chances that in 2 selections, none are red?

 

  4   *   3   =   12   =  2 

 10       9        90       15

 

1 - 2/15 = 15/15 - 2/15 = 13/15