a fair die is tossed. A is the event that the outcome is odd. B is the event that the outcome is even. C is the event that the outcome is ess than 4.

The question is incomplete. Below is the complete question

"A fair die is tossed. A is the event that the outcome is odd. B is the event that the outcome is even. C is the event that the outcome is less than 4. Determine P (A), P (B), P (C), P (A∩B), P (B∩C), P (A|B), P (A|C), P (B|C).

answers:

a. 1/2

b. 1/2

c. 1/2

d. 0

e. 1/6

f. 0

g. 2/3

h. 1/3

Step-by-step explanation:

lets write out the probability of each event

a. A=outcome is odd

A={1,3,5}

P (A) = 1/2

b. B=outcome is even

B={2,4,6}

P (B) = 1/2

c. C=outcome is less than 4

C={1,2,3}

P (C) = 1/2

d. P (AnB) = {its odd and even i. e what is common between set A and B}

Therefore, P (AnB) is a null set i. e P (AnB) = { }=0

e. BnC = {2} i. e elements common between set B and C

Hence P (BnC) = 1/6

f. PA = P (AnB) / P (B) since P (AnB) = 0, P (B) = 1/2. then, P (A|B) = 0

g. P (A|C) = P (AnC) / P (C) since P (AnC) = 1/3, P (C) = 1/2. therefore, P (A|C) = 2/3

h. P (B|C) = P (BnC) / P (C), since P (BnC) = 1/6, P (C) = 1/2. therefore, P (B|C) = 1/3