[College Introductory Statistics] Trouble with Conditional Probability
I can only make it so far on each, but I will show what I have.
- Prove for any three events A, B, C:
P (ABC) ≥ P (A) + P (B) + P (C) – 2.
Answer Attempt: P(A) * P(B) * P(C)
P(A)*P(B)*P(C) >= P(A)+P(B)+P(C) -2
P(A ∩ B ∩ C) >= P (A) + P (B) + P (C) – 2.
But I don't know where to do from there
- Bob has a pack of well-shuffled 52 cards, and keeps picking cards
out
at random until he draws the Ace of spades. What is the
probability
that the Ace of Spades is the 25th. card to be pulled out if:
A. Bob discards each of the first 24 cards after he pulls it out?
B. Bob replaces each card he pulls out if it is not the Ace of Spades?
Answer Attempt: A. 1/52?
B. Π from i = 0 to 24 (51-i)/(52) = ((51!/27!)/(52^24)) = .000932
.09 percent seems wrong
- A Peruvian human sacrificial temple, near Lima, Peru, has three
levels, levels J, M, and H, where tourists have the only access to
the temple.
The probabilities that a tourist visiting the temple will visit the
different levels are:
Visit level J: 0.74
Visit level M: 0.70
Visit level H: 0.62
Visit levels J and M: 0.52
Visit levels J and H: 0.46
Visit levels M and H: 0.44
Visit levels J and M and H: 0.34.
Find the probabilities that a person visiting the temple will:
A. Visit level M given that he will go to level J.
B. Visit level H given that he will go to level J and level M.
C. Not visit level J given that he will visit level M or visit
level H.
D. Visit level H and visit level J given that he will not visit level
M.
Answer Attempt: A. P(M | J) = (P(MJ))/(P(J)) = .52/.74
B. P(H | JM) = P(HMJ)/P(JH) = .32/52
C. P(not J | M) || P (not J | H) = P(notJM)/P(M) || P(notJH)/P(H) = .48/.70 and .54/.62 respectively
D. (HJ | notM) = P(HJnotM)/P(notM) but I can't find the values of these