Question

A bag contains 10 marbles: 2 are green, 2 are red, and 6 are blue. Bob chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles he chooses are green? Wrote the answer as a fraction in simplest form.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

total marbles = 10

green = 2

red = 2

blue = 4

probability that both marbles he chooses are green = ?

Step 02:

simple probability = favorable outcomes / total outcomes

1st event: probability of green marble

pg1 = 2 / 10

2nd event: probability of green marble

pg2 = 1 / 9

total probability:

total probability = pg1 + pg2

total probability = 2/10 + 1/9

`tp\text{ = }(2)/(10)+(1)/(9)=\frac{(2\cdot9)\text{ + (1}\cdot10)}{(10\cdot9)}=(18+10)/(90)=(28)/(90)=\text{ }(14)/(45)`

The answer is:

The probability that both marbles he chooses are green is 14 /45