A box contains 10 red balls and 10 green balls. Five draws are made without replacement.
Find the probability of selecting 4 balls of the same colour.
could be 4 green and one red , or, 4 red and 1 green
prob(the stated event) = ( C(10,4)*C(10,1) + C(10,4)*C(10,1) )/C(20,5)
= .....
To find the probability of selecting 4 balls of the same color, we need to consider two scenarios: selecting 4 red balls and selecting 4 green balls. We will calculate the probability for each scenario and then add them together.
First, let's calculate the probability of selecting 4 red balls:
The total number of balls in the box is 10 red + 10 green = 20 balls.
To select 4 red balls, we need to consider the number of possible ways to select 4 balls out of the 10 red balls. This can be calculated using the combination formula, denoted as "nCr", which calculates the number of ways to choose 'r' items from a set of 'n' items.
In this case, we want to select 4 red balls out of a total of 10 red balls.
The number of ways to choose 4 items out of 10 is calculated as:
10C4 = 10! / (4! * (10-4)!) = 210
Now, we need to calculate the number of ways to select any 4 balls out of the total 20 balls in the box. This can also be calculated using the combination formula.
The number of ways to choose 4 items out of 20 is calculated as:
20C4 = 20! / (4! * (20-4)!) = 4845
Now, we can calculate the probability of selecting 4 red balls:
Probability of selecting 4 red balls = (number of favorable outcomes / total number of possible outcomes) = (210/4845)
Next, let's calculate the probability of selecting 4 green balls:
The process is similar to the one used for calculating the probability of selecting 4 red balls.
The number of ways to select 4 green balls out of the 10 green balls is:
10C4 = 10! / (4! * (10-4)!) = 210
The number of ways to choose 4 items out of the total 20 balls is:
20C4 = 20! / (4! * (20-4)!) = 4845
Therefore, the probability of selecting 4 green balls is: Probability of selecting 4 green balls = (number of favorable outcomes / total number of possible outcomes) = (210/4845)
Lastly, since we want either 4 red balls or 4 green balls, we need to add the probabilities of each scenario together.
The total probability of selecting 4 balls of the same color is:
Probability of selecting 4 balls of the same color = Probability of selecting 4 red balls + Probability of selecting 4 green balls
You can now plug in the calculated probabilities to find the final answer.