distrib /40 points) Consider the following r P(a) 0 0.10025 1 0.14575 2 0.15825

Question

distrib /40 points) Consider the following r P(a) 0 0.10025 1 0.14575 2 0.15825 3 0.11350 4 0.12425 5 0.10225 60.12185 70.13390 der the events A-(0, 1, 3, 5, 6), B = {o, 2, 3, 4). and Ce(1, 5, 7). ne P(4), the probability that event A will occur, and a. Determi event 3 will occur. Hint: Add the probabilities correspon elements in each set. P(B), the probability that to each of the b. Determine P(A and B), the probability that both event A and event B will occur. c. Determine P(A or B), the probability that either event A or event B will occur. d. Determine P(CIA), the conditional probability that event C will occur given that eventA has already occurred

Explanation / Answer

(a) Given pdf:

x                    P(x)

0                      0.10025

1                     0.14575

2                    0.15825

3                   0.11350

4                  0.12425

5                  0.10225

6                  0.12185

7                0.13390

(a)

Given:

A = {0.1.3.5.6}

So,

P(A) = 0.10025 +0.14575 + 0.11350 + 0.10225 + 0.12185 = 0.58360

B = {0,2,3,4}

So,

P(B) = 0.10025 + 0.15825 +0.11350 + 0.12425 = 0.49625

(b) A and B = {0,3}

So,P(A and B) = 0.10025 + 0.11350 = 0.21375

(c) A or B = {0,1,2,3,4,5,6} = 0.86610

(d) P(C/A) = P(C and A)/P(A)

C and A = {1,5}

So,

P(C and A) = 0.14575 + 0.10225 = 0.24800

P(A) = 0.58360

Substituting the values, we get:

P(C/A) = 0.24800/0.58360 = 0.4249

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