Answer to Question #198553 in Statistics and Probability for fahmida

Question

5) At the end of performance evaluation period; the production manager found that 5 of the 50 workers completed work late, 6 of the 50 workers assembled a defective part, and 2 of the 50 workers completed work late and assembled a defective part. Suppose, L is the event that work is completed late and D is the event that assembled part is defective. a. Find P (L).b. Find P (D).c. Find P (L ∩ D).

7) Consider tossing two coins. a. Develop the sample space. b. Find out the probability of getting at least one head. c. What is the probability of getting two tails? d. What is the probability of getting one head?

8)An experiment has four equally likely outcomes: E1, E2, E3, and E4. a. What is the probability that E3 occurs? b. What is the probability that any two of the outcomes occur? c. What is the probability that any three of the outcomes occur?

Answer 1

5)

a.

$$P(L)=\dfrac{N(L)}{N}=\dfrac{5}{50}=0.1$$

b.

$$P(L)=\dfrac{N(D)}{N}=\dfrac{6}{50}=0.12$$

c.

$$P(L)=\dfrac{N(L\cap D)}{N}=\dfrac{2}{50}=0.04$$

7)

a.

$$S=\{HH, HT, TH, TT\}$$

b.

$$P(at\ least\ 1H)=\dfrac{3}{4}=0.75$$

c.

$$P(TT)=\dfrac{1}{4}=0.25$$

d.

$$P(1H)=\dfrac{2}{4}=\dfrac{1}{2}=0.5$$

8)

a.

$$P(E_2)=\dfrac{1}{N}=\dfrac{1}{4}=0.25$$

b.

$$P(2\ any \ outcomes)=\dfrac{2}{N}=\dfrac{2}{4}=\dfrac{1}{2}=0.5$$

c.

$$P(3\ any \ outcomes)=\dfrac{3}{N}=\dfrac{3}{4}=0.75$$