Question

PROBLEM 3-1, Aduls in a community ether they smoke E rom high school [B 1.See Table 3-5. (a) Calculate P(A | B)and P(A | B). (b) Calculate P(B | A)and P(BIA (c) Determine whether events A and B are independent. smoke [A'1, and whether they graduated from high school [B] or didn't graduate f TABLE 3-5: Table for Problem 3-19 High schoo Not high school Row graduate [B] graduate [B] totals 60% 40% 20% Smokes [A] Doesn't smoke [A'] 40% 30% Column totals 70% 30% 100% Answer (a) 4/7, 2/3 (b) 2/3, 3/4 (c) No PROBLEM 3-20 A fair die is tossed three times in succession. (a) How many elements are there in the most subdivided sample space? (b) Let A be the event of obtaining an ace [face with one dot] on exactly the first and third tosses. Calculate P(A). (c) Let B be the event of obtaining fewer than three dots on exactly the first and second tosses. Calculate P(B).

Answer 1

Ans:

a)

P(A/B)=P(A and B)/P(B)=0.4/0.7=4/7

P(A/B')=P(A and B')/P(B')=0.2/0.3=2/3

b)

P(B/A)=P(A and B)/P(A)=0.4/0.6=4/6=2/3

P(B/A')=P(A' and B)/P(A')=0.3/0.4=3/4

c)

To be independent:

P(A and B)=P(A)*P(B)

P(A and B)=0.4

P(A)*P(B)=0.6*0.7=0.42

As,P(A and B) is not equal to P(A)*P(B),so events A and B are not independent.