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Calculating Probabilities Using Probability Rules


New member
Oct 25, 2009
Can someone please review my work and let me know if I'm doing them right? If not, please let me know how I can fix it. Thank you.

A, B, and C are events of a probability experiment. Given that
P(A)=0.25, P(B)=0.75, P(C)=.35
determine the following:

a. P(A or B) if P(A and B) = 0.27

P(A or B) = P(A) + P(B) - P(A and B)
= .25 + .75 - .27
= .73

b. P(A or C) if A and C are mutually exclusive

P(A) + P(C)
P(.25) + P(.35)
= .6

c. P(B and C) if P(B or C) = 0.15

.15 - .75 + .35
= -.4

d. P(C[sup:ryo85qwa]c[/sup:ryo85qwa])

P(C[sup:ryo85qwa]c[/sup:ryo85qwa]) = 1 - P(C)= 1 - .35
= .65

e. P(A and C) if A and C are independent.

P(A) . P(C)
P(.25) . P(.35)
= .088


Elite Member
Jan 28, 2005
Hello, boydoineedhelp!

Only part (c) is off . . . Good work!

\(\displaystyle A, B,\text{ and }C\text{ are events of a probability experiment.}\)

\(\displaystyle \text{Given: }\;P(A)\,=\,0.25,\;\;P(B)\,=\,0.75,\;\; P(C)\,=\,0.35\)

\(\displaystyle \text{Find: }\;(c)\;P(B \cap C)\:\text{ if }P(B \cup C) \,=\, 0.15\)

\(\displaystyle \text{Use the formula: }\;\underbrace{P(B \cup C)}_{0.15} \;=\; \underbrace{P(B)}_{0.75} + \underbrace{P(C)}_{0.35} - P(B \cap C)\)

\(\displaystyle \text{We have: }\:0.15 \;=\;0.75 + 0.35 - P(B \cap C)\)

\(\displaystyle \text{Therefore: }\:p(B \cap C) \:=\:0.75 + 0.35 - 0.15 \:=\:0.95\)



New member
Oct 25, 2009
Thanks! I knew that question C was definitely wrong because it was a negative. I actually figured out the same answer (.95) you got late last night. I wasn't sure if .95 was right since the wording for the problem was different and I was not sure how to show the breakdown of the formula. Now I see how it comes out to that. Thanks again. I appreciate it.