Question

6-10 help

6. If P(A) 0.4, P(B) 0.5, and P(A UB) 0.7, find a. P(A n B) b. P(A' U B') 7. A coin is tossed 4 times and the sequence of heads and tails is observed a. b. What is the sample space S for this experiment? Consider the following events: A [at least 3 heads) B- (at most 2 heads) C = {heads on the 3rd toss) D- (1 head and 3 tails) If the outcomes in S are equally likely, find the following: i. P(A) ii. P(An B) v. P(D) vi. P(AUC) vii. P(B nD) 8. Construct a Venn Box Diagram for the following scenario and use it to answer the question. There are 28 people in your family consisting of 18 adults, 13 females, and 11 who have red hair. There are 11 adult females, si of whom have red har. How many male children without red hair are in the family? 9. A survey of a group's viewing habits over the last year revealed the following information: a, 28% watched gymnastics b, 29% watched basketball C. 19% watched soccer d. 14% watched gymnastics and baseball 12% watched baseball and soccer e, f. 10% watched gymnastics and soccer 8% watched all three sports g, Calculate the percentage of the group that watched none of the three sports during the last year. 10. If P(A) 0.4, P(B) 0.5, and P(AnB)-0.3, find a. P(A U B) b. P(A n B') c. P(A' U B').

Answer 1

6.) P(A and B) = P(A) + P(B) - P(A or B) = 0.2

     P(A' or B') = P(A') + P(B') - P(A' and B') = 0.3

7.) a. Sample space -

P(A) = 5/16, P(B) = 11/16, P(C) = 8/16, P(D) = 4/16

i. P(A) = 5/16 = 0.3125

ii. P(A and B) = 0

iii. P(B) = 11/16 = 0.6875

iv. P(A and C) = 4/16 = 0.25

v. P(D) = 4/16 = 0.25

vi. P(A or C) = 9/16 = 0.5625

vii. P(B and D) = 4/16 = 0.25