suppose a hat containing 100 balls consists of 20blue ball,30yellow balls,30red balls and 20green balls.a sample of 5 balls is drawn from the hat one by one without replacement.what is the probability that there will be 2blue balls in the sample
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
20/100 * 19/99 * (98-18)/98 * (97-18)/97 * (96-18)/96 = ?
To find the probability of drawing 2 blue balls from the sample, you need to calculate the total number of favorable outcomes (drawing 2 blue balls) divided by the total number of possible outcomes (drawing any 5 balls).
To do this, follow these steps:
Step 1: Find the total number of ways to choose 5 balls from the 100 balls in the hat. This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
where n represents the total number of balls and r represents the number of balls chosen. In this case, n = 100 (total balls) and r = 5 (balls chosen).
C(100, 5) = 100! / (5! * (100-5)!)
Step 2: Calculate the total number of ways to draw 2 blue balls from the 20 blue balls in the hat. Again, this can be calculated using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
where n represents the total number of blue balls and r represents the number of blue balls drawn. In this case, n = 20 (total blue balls) and r = 2 (blue balls drawn).
C(20, 2) = 20! / (2! * (20-2)!)
Step 3: Multiply the results from Step 2 and Step 3 to get the total number of favorable outcomes (drawing 2 blue balls from the sample):
Favorable outcomes = C(20, 2) * C(80, 3)
Step 4: Finally, calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total possible outcomes = [C(20, 2) * C(80, 3)] / C(100, 5)
Now, you can substitute the values into the equation and solve for the probability.