the probability that a television containt 0, 1, or 2 defects is 0.88, 0.08, and 0.04, respectively. in a sample of 16 television, find the probability that 9 will have 0 defects, 4 will have 1 defect, and 3 will have 2 defects.
To find the probability that a specific combination occurs in a sample, we need to multiply the individual probabilities together.
In this case, we want to find the probability that 9 televisions will have 0 defects, 4 televisions will have 1 defect, and 3 televisions will have 2 defects.
We are given that the probability of having 0 defects is 0.88, the probability of having 1 defect is 0.08, and the probability of having 2 defects is 0.04.
To calculate the probability of the specific combination, we multiply these probabilities together:
P(9 TVs with 0 defects) = (0.88)^9
P(4 TVs with 1 defect) = (0.08)^4
P(3 TVs with 2 defects) = (0.04)^3
So, the overall probability is:
P(all desired combinations) = P(9 TVs with 0 defects) * P(4 TVs with 1 defect) * P(3 TVs with 2 defects)
= (0.88)^9 * (0.08)^4 * (0.04)^3
To get the final answer, we can calculate this expression using a calculator or computer software.