Question

There are 2 green marbles, 4 blue marbles, 1 red marble, and 8 yellow marbles in a bag. Once a marble is drawn, it is NOT replaced. Find the probability of the outcome. P(a blue marble then a green marble)

answers are:
4/105
6/29
8/225
1/35

Answer 1

`(4)/(105)`

Explanation:

In total there are 2 + 4 + 1 + 8 = 15 marbles

The probability of taking a blue is number of blue divided by number of total, so that would be

`(4)/(15)`

Since, it is not replaced, we can now say that there are 1 less marbles in the bag (since we took out a blue). Now probability of getting a green marble is:

`(2)/(14)=(1)/(7)`

In probability, "and" means "multiplication" and "or" means "addition".

Since we want Probability of blue marble and green marble, we multiply both:

`(4)/(15)*(1)/(7)=(4)/(105)`

THus, first answer choice is right.

Answer 2

P(a blue marble then a green marble) is 4/105 ⇒ 1st answer

Explanation:

* Lets explain how to solve the problem

- There are 2 green marbles

- There are 4 blue marbles

- There are 1 red marble

- There are 8 yellow marbles

- Once a marble is drawn, it is NOT replaced

- We need to find P(a blue marble then a green marble)

* At first lets find the total number of marbles by adding all color

∵ There are 2 green , 4 blue , 1 red and 8 yellow

∴ The total number of marbles = 2 + 4 + 1 + 8 = 15

∴ There are 15 marbles in the bag

∵ Probability = number of events/number of all outcomes

∵ There are 4 blue marbles

∴ The probability of chosen a blue marble is P(blue) = 4/15

∵ Once a marble is drawn, it is NOT replaced

∴ The total number of marbles = 15 - 1 = 14 marbles

∵ The number of green marbles is 2

∴ The probability of chosen a green marble is P(green) = 2/14

∵ P(a blue marble then a green marble) = P(blue) . P(green)

∵ P(blue) = 4/15

∵ P(green) = 2/14

∴ P(a blue marble then a green marble) = (4/15)(2/14) = 4/105

* P(a blue marble then a green marble) is 4/105