A basket of 50 golf balls contains 22 yellow balls. If 8 balls are selected at random from the basket, determine the probability that none of those selected is a yellow ball.
42/50 is the probability.
28/50 * 27/49 ...
= (28*27*26*25*24*23*22*21)/(50*49*48*47*46*45*44*43)
= (28!/(28-8)!) / (50!/(50-8)!)
= 117/20210
= 0.005789
To determine the probability that none of the selected balls is yellow, we need to calculate the number of favorable outcomes (i.e., the number of ways to select 8 balls from the 50 that are not yellow) and the total number of possible outcomes (i.e., the total number of ways to select 8 balls from the 50 in the basket).
Let's break down the solution into steps:
Step 1: Calculate the total number of ways to select 8 balls from the 50 in the basket. We can use the combination formula, also known as "nCr," which calculates the number of combinations of n items taken r at a time. In this case, n = 50 (the total number of balls) and r = 8 (the number of balls to be selected).
The formula for nCr is:
nCr = n! / (r!(n-r)!)
Substituting the values, we get:
50C8 = 50! / (8!(50-8)!)
Step 2: Calculate the number of ways to select 8 balls that are not yellow. Since there are 22 yellow balls in the basket, the remaining balls that are not yellow would be 50 - 22 = 28.
Using the same combination formula, with n = 28 (number of non-yellow balls) and r = 8 (number of balls to be selected), we calculate:
28C8 = 28! / (8!(28-8)!)
Step 3: Calculate the probability. Now that we have the number of favorable outcomes (the number of ways to select 8 non-yellow balls) and the total number of possible outcomes (the number of ways to select 8 balls), we can calculate the probability.
The probability is equal to the number of favorable outcomes divided by the total number of possible outcomes:
Probability = (number of favorable outcomes) / (total number of possible outcomes)
= 28C8 / 50C8
So, to find the probability, divide the value of 28C8 by the value of 50C8.
Using a calculator or a mathematical software, evaluate the quotient 28C8 / 50C8 to get the final probability.