A bag contains 4 blue marbles and 4 red marbles. If three marbles are drawn in a row without replacement, find the probability that the marbles will be the same colour?

Max, Charlotte, Markus -- please use the same name for your posts.

To have the same colour, you need

either BBB or RRR

Find the prob of each case, then add them up

To find the probability that the marbles drawn will be the same color, we first need to determine the total possible outcomes and the favorable outcomes.

Total Possible Outcomes:
When drawing three marbles without replacement, the total number of outcomes can be calculated using the concept of combinations.

The total number of marbles available is 8 (4 blue + 4 red), and we need to choose 3 marbles at once. Therefore, the total possible outcomes can be calculated as "8 choose 3," which is denoted as C(8, 3) or 8C3, and equals 56.

Favorable Outcomes:
To calculate the favorable outcomes, we need to consider two cases:
1. Three blue marbles: There are 4 blue marbles in the bag, and we need to choose all 3. This can be calculated as "4 choose 3," or 4C3, which equals 4.
2. Three red marbles: Similar to the previous case, there are 4 red marbles, and we need to choose all 3. This can also be calculated as "4 choose 3," or 4C3, which equals 4.

Therefore, the favorable outcomes are the sum of the favorable outcomes from the two cases, which is 4 + 4 = 8.

Probability:
The probability of an event is given by the formula: Probability = (Number of favorable outcomes) / (Number of total possible outcomes)

Using this formula, the probability of drawing three marbles of the same color can be calculated as:
Probability = (Number of favorable outcomes) / (Number of total possible outcomes)
= 8 / 56
= 1 / 7

Hence, the probability that the marbles drawn without replacement will be of the same color is 1/7.