Question

The table below shows the number of marbles of different colors in a bag:

Marble Experiment



Color of 
Marbles 

Number of 
Marbles 



Red

5 


White

8 


Black

2 



Deja draws a marble from the bag randomly without looking. She then draws another marble from the bag without replacing the first one. Which expression shows the probability of drawing red marbles in both the trials?


5 over 15 multiplied by 4 over 14 
5 over 15 multiplied by 4 over 15
5 over 15 added to 4 over 14 
5 over 15 added to 4 over 15

Vincent is giving cakes to some children at a carnival. He has 2 strawberry cakes, 6 pineapple cakes, and 7 chocolate cakes. If Vincent selects a cake randomly without looking, what is the probability that he will give a pineapple cake to the first child and then a strawberry cake to the second child?

6 over 15 multiplied by 2 over 14 is equal to 12 over 210 
6 over 15 plus 2 over 14 is equal to 114 over 210
6 over 15 multiplied by 2 over 15 is equal to 12 over 225
6 over 15 plus 2 over 15 is equal to 8 over 15

Answer 1

8-2
$\div$
15

Answer 2

There are a total of 5+8+2=15 marbles.  There's a 5/15 chance of drawing a red marble in the first trial.  Then, there are 4 red marbles and 14 total marbles left, so afterwards, there's a probability of 4/14 that the second marble is red.  The probability overall is found by multiplying these together, so the first answer is the best.

There are 2+6+7=15 cakes.  There's a 6/15 chance that the first cake selected will be a pineapple cake, and then a 2/14 chance that the second cake selected will be a strawberry cake, by the same logic as above.  This is equal to 12/210.  The first answer is the best option.