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.

"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. P{A|B}= 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