Question

The probabilities of a, b and c becoming managers are 4 9 , 2 9 and 1 3 respectively. the probabilities that the employment insurance scheme will be introduced if a, b, c become managers are 3 10 , 1 2 and 4 5 respectively.

what is the probability that the employment insurance scheme will be introduced?

Answer 1

To find the probability that the employment insurance scheme will be introduced, you calculate the sum of the probabilities of each potential manager (A, B, C) times the probability that they will introduce the scheme, which results in a total probability of 0.56.

Step-by-step explanation:

The probability that the employment insurance scheme will be introduced can be calculated by using the law of total probability, which takes into account the probability of each individual (A, B, C) becoming a manager and the probability of that person introducing the scheme.

The calculation is as follows:

1. Probability (A becomes manager) × Probability (scheme is introduced by A) = ⅔ × ⅓
2. Probability (B becomes manager) × Probability (scheme is introduced by B) = ⅙ × ½
3. Probability (C becomes manager) × Probability (scheme is introduced by C) = ⅓ × ⅔

Add these individual probabilities together to obtain the total probability:

⅔ × ⅓ + ⅙ × ½ + ⅓ × ⅔ = ⅖ × 3 + ⅙ × 5 + ⅓ × 8 = ⅖ + ⅙ + ⅓ = ⅗ (or 0.56).

Therefore, the probability that the employment insurance scheme will be introduced is 0.56.