can you solve these problems?

Question

1.In the work force of a large company, 70% of the employees are high school graduates, 8% are supervisors, and 5% are both supervisors and high school graduates. From this information, answer these questions. (a) if the employee is high-school graduates, what is the probability he is a supervisors? (b) if the employee is not a high school graduate, what is the probability he is a supervisor?
2.A town has 2 fire engines operating independently. The probability that a specific engine is available when needed is 0.96.
a.What is the probability that neither is available when needed?
b.What is the probability that a fire engine is available when needed?
3.Two cards are drawn from a well shuffled ordinary deck of 52 cards. Find the probability that they are both aces if the first card is a) replaced , b) not replaced
4.Two cards are drawn from a well shuffled ordinary deck of 52 cards. Find the probability that they are both aces if the first card is a) replaced , b) not replaced.

Answer 1

©
1.a. 0.05/0.7 = 7.14%
b. since 8% are supervisors, 5% are both supervisor and high school grad, then
3% are supervisor and not high school grad.
prob = 0.03/0.3 = 10%

2.a. Prob = 0.04 + 0.04 - 0.04*0.04 = 7.84%

b. Prob = .96 + .96 - .96*.96
= 99.84%

3.a. 4/52*3/51
b. (4/52)^2

4. repeated question

Answer 2

Use Venn Diagrams for the first and logic for the second.

Answer 3

1a. 5/70
1b. 3/30

2a. 0.04 * 0.04
2b. (0.96 * 0.04) * 2

3a. 4/52 * 4/52
3b. 4/52 * 3/51

Answer 4

a) 30/100
b)30/100