Suppose 4 news anchors are randomly selected. Assume the appropriate requirements are met. If the chances of reporters working for one news anchor is 0.60, find the probability it works for three of them.
Is the probability the same for all 4?
What does the "it" refer to?
To find the probability that three out of four news reporters work for one news anchor, we can use the concept of binomial probability.
The binomial probability formula is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of having exactly k successes
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success for each trial
- n is the total number of trials
In this case, we want to find the probability of three out of four reporters working for one news anchor, so n = 4 and k = 3. The probability of a reporter working for one news anchor is given as p = 0.60.
First, let's calculate the number of combinations for selecting three reporters out of four:
C(4, 3) = 4! / (3! * (4-3)!)
= 4! / (3! * 1!)
= 4
Now, we can substitute the values into the binomial probability formula:
P(X = 3) = C(4, 3) * (0.60)^3 * (1-0.60)^(4-3)
P(X = 3) = 4 * 0.60^3 * 0.40^1
P(X = 3) = 4 * 0.216 * 0.40
P(X = 3) = 0.3456
Therefore, the probability that three out of four news reporters work for one news anchor is approximately 0.3456 or 34.56%.