Number cards

Question

The number cards shown below are placed inside of a box.

 

1,2,2,5,6,7,8,8,8,10

 

One card will be removed at a time and not replaced 

 

A) what is the probability the first two cards removed from the box will both have an even number?

 

B) What is the probability that the first odd numbered card selected will be the third card removed from the box?

Answer 1

A) There are 7 even-numbered cards out of 10.  So the probability that the first card is even is 7/10.

 

Once an even-numbered card is removed, there are now 9 cards left, of which 6 are even.  So the probability that the second card is also even will be 6/9 = 2/3.

 

So the probability that BOTH will be even is 7/10 * 2/3 = 14/30 = 7/15

 

B) In order for the first odd numbered card to be the third card removed, two things have to be true:

 

1. The first two cards are even.  We already know that the probability of that is 7/15.

2. The third card is odd.  After the first two cards are removed and they are both even, there are now 8 cards left of which 5 are even, and 3 are odd.  So the probability of the third card being odd is 3/8.

 

So the probability of the first two cards being even AND the third card being odd is 7/15 * 3/8 = 21 / 120 = 7/40.