You have 1 red marble, 1 blue marble, 1 yellow marble and 1 white marble. You draw 2 marbled out of the bag without replacing. What is the probability that you may choose 1 red marble?

Question

You have 1 red marble, 1 blue marble, 1 yellow marble and 1 white marble. You draw 2 marbled out of the bag without replacing. What is the probability that you may choose 1 red marble?

Answer 1

To find the probability of picking 1 red marble out of 2 marbles without replacement, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:
When drawing 2 marbles without replacement, the total number of possible outcomes is the number of ways we can choose any 2 marbles out of the 4 marbles in the bag. This can be calculated using the combination formula:

nCr = n! / ((n-r)! * r!)

Here, n represents the total number of items (4 marbles) and r represents the number of items chosen (2 marbles).

So, the total number of possible outcomes is:

4C2 = 4! / ((4-2)! * 2!) = 6

Number of favorable outcomes:
To find the number of favorable outcomes, we need to consider the scenarios where we choose 1 red marble out of 2 marbles.

Scenario 1: Choose red, then any other color.
We can either choose the red marble first and then any other color (blue, yellow, or white), or we can choose the red marble second and any other color as the first pick. This gives us 2 favorable outcomes.

Scenario 2: Choose any other color, then red.
Similarly, we can either choose any other color first and then the red marble, or we can choose the red marble first and any other color as the second pick. Again, we have 2 favorable outcomes.

So, the number of favorable outcomes is 2 + 2 = 4.

Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.

Therefore, the probability of choosing 1 red marble is:

Number of favorable outcomes / Total number of possible outcomes = 4 / 6

Simplifying it further:

4 / 6 = 2 / 3

So, the probability of choosing 1 red marble is 2/3.

Answer 2

There are 6 ways you can draw the two marbles to include one red:

RB,RY,RW,BR,YR,WR

There are 4P2 = 12 ways to draw any two marbles

So, P(one red) = 6/12 = 1/2