An insurer offers a health plan to the employees of a large company. As part of this plan, the individual employees may choose two of the supplementary covaerges A, B and C or they may choose no supplementary coverage. The proportions of the company's employees that choose coverage A, B and C are 1/4 ,1/3 and 5/12 respectively. Determine the probability that a randomly chosen employee will choose no supplementary coverage.
To determine the probability that a randomly chosen employee will choose no supplementary coverage, we first need to find the probability of each employee choosing each type of supplementary coverage.
Given that the proportions of the company's employees that choose coverage A, B, and C are 1/4, 1/3, and 5/12 respectively, we can calculate the probability for each option as follows:
Probability of choosing coverage A = 1/4
Probability of choosing coverage B = 1/3
Probability of choosing coverage C = 5/12
Since the employee can choose two out of the three options or choose no supplementary coverage, the remaining probability (1 - P(A) - P(B) - P(C)) will represent the probability of choosing no supplementary coverage.
Let's calculate this:
Probability of choosing no supplementary coverage = 1 - (P(A) + P(B) + P(C))
Substituting the given probabilities, we have:
Probability of choosing no supplementary coverage = 1 - (1/4 + 1/3 + 5/12)
To find the common denominator, we need to determine the least common multiple (LCM) of 4, 3, and 12, which is 12. Now we can rewrite the equation:
Probability of choosing no supplementary coverage = 1 - (3/12 + 4/12 + 5/12)
Combining the fractions with the common denominator, we get:
Probability of choosing no supplementary coverage = 1 - (12/12)
Simplifying further, we have:
Probability of choosing no supplementary coverage = 1 - 1
Therefore, the probability of a randomly chosen employee choosing no supplementary coverage is 0.
This means that there is no chance of a randomly chosen employee choosing no supplementary coverage based on the given proportions.