Chapter 14-Statistics -MyMathLab
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Find the probabilities for parts (a) through (h) below and express your results in words. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. A. event a card higher than 8 is selected B. event a king is selected C. event a diamond is selected
1) The probability that a KING IS SELECTED given that a card higher than 8 is not selected is 0. 2) The probability that A card higher than 8 is selected is 6/13 3) Find P(A/B)- The probability that a card higher than 8 is selected, given that a KING IS selected is 1. 4) find P(AC) The probability that A card higher than 8 is selected, given that a DIAMOND is Selected is 6/13 5)THE probability a card HIGHER THAN 8 IS selected given that A KING IS NOT selected is 5/12.
A joint probability distribution is shown below. Determine both P(C2|R1) and P(R1|C2). C1 C2 C3. P(Rj) R1 0.25 0.06 0.14 0.45 R2. 0.14. 0.24 0.17 0.55 P(Ci) 0.39 0.30 0.31 1.00
P(C2/R1= 0.133 2) P(R1/C2= 0.200
Suppose that E and F are two events and that P(E & F)=0.2 and P(E)=0.5. What is P(F|E)?
P(FIE) .4
Suppose that A, B, and C are independent events such that P(A)=0.3, P(B)=0.2, and P(C)=0.5. Find P(A & B & C).
0.3X0.2X0.5=0.03
Two cards are drawn at random from an ordinary deck of 52 cards. Determine the probability that both cards are clubs if a. the first card is replaced before the second card is drawn. b. the first card is not replaced before the second card is drawn.
1) 0.063 2) 0.059
Two cards are drawn at random from an ordinary deck of 52 cards. Determine the probability that both cards are hearts if a. the first card is replaced before the second card is drawn. b. the first card is not replaced before the second card is drawn.
1) 0.063 2) 0.059
Two cards are drawn at random from an ordinary deck of 52 cards. Determine the probability that both cards are clubs if a. the first card is replaced before the second card is drawn. b. the first card is not replaced before the second card is drawn.
1) 0.063 2)0.059
Information on the weights and years of experience for a football team was obtained. The given contingency table provides a cross-classification of those data. Compute the following conditional probabilities directly; that is, do not use the conditional probability rule. A player on the football team is selected at random. Complete parts (a) through (e) below weight Y1. Y2. Y3. Y4. TOTAL -200 6 5. 1. 0. 12 200-300 7. 10. 16. 8. 41 +300 0 8. 8. 0. 16 TOTAL 13. 23. 25. 8. 69
1) 0.188 2) 0.174 3) 0.5 4) 0.462 5) 18.8% 6) 17.4% 7) 50% 8) 46.2
Two cards are drawn at random from an ordinary deck of 52 cards. Determine the probability that both cards are black if a. the first card is replaced before the second card is drawn. b. the first card is not replaced before the second card is drawn.
1) 0.25 2) 0.245
Below is a joint probability distribution for the members of a state congress by legislative group and political party. The "other" category includes Independents and vacancies. REP. SEN. P(P1) Democrats-P1 0.371. 0.136 0.507 Republicans-P2 0.401 0.087 0.488 Other-P3 0.002 0.003 0.005 P(CJ) 0.774 0.226 1.000
1) 0.507 2) 0.774 3) 0.371 4) NO
Suppose that A and B are independent events such that P(A)=0.6 and P(B)=0.8. Find P(A & B).
1) 0.6x0.8=0.48
Suppose P(A)=0.9 and P(B|A)=0.15 Find P(A & B).
1) 0.9x0.15=0.135
A hand of five-card poker consists of an unordered arrangement of five cards from an ordinary deck of 52 playing cards. Complete parts (a) through (e) below.
1) How many unordered five-card poker hands are possible? There are 2,598,9602 different five-card draw poker cards 2) How many different hands consisting of one four and four jacks are possible? There are 44 different hands consisting of one four and four jacks. 3) The hand in part (b) is an example of a four of a kind: four cards of one denomination and one of another. How many different four of a kinds are possible? There are 624 different four of a kinds. 4) The probability of being dealt a four of a kind is 0.00024 5) For an ordered arrangement of five cards, there are 311,875,200 different five-card hands, 480 different hands consisting of one four and four jacks, 74,880 different four of a kinds, and the probability of being dealt a four of a kind is about 0.00024. Choose the correct answer below. C. There are fewer possible hands for unordered hands, but there are also fewer possible four of a kinds. The probability of a four of a kind is the same. This is the correct answer.
A contingency table is shown below. Determine both P(C2|R2) and P(R2|C2). C1 C2 TOTAL R1 4, 7 11 R2 9. 7. 16 total: 13. 14. 27
1) P(C2|R2) = 7/ 16 2) P(R2|C2). = 1/2
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Find the probabilities for parts (a) through (h) below and express your results in words. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. A event a card higher than 9 is selected B event a card between 7 and 10, inclusive, is selected C event a heart is selected
1) The probability that a card between 7 and 10, inclusive, is selected is 4/13 2)the probability that a card between 7 and 10, inclusive, is selected, given that a card higher than 9 is selected is 1/5 3) The probability that a card between 7 and 10, inclusive, is selected, given that a heart is selected is 4/13 4) The probability that a card between 7 and 10, inclusive, is selected, given that a card higher than 9 is not selected is 3/8 5)The probability that a card higher than 9 is selected is 5/13 6) The probability that a card higher than 9 is selected, given that a card between 7 and 10, inclusive, is selected is 1/4 7) The probability that a card higher than 9 is selected, given that a heart is selected is 5/13 8) The probability that a card higher than 9 is selected, given that a card between 7 and 10, inclusive, is not selected is 4/9
One card is selected at random from an ordinary deck of 52 playing cards. Events A, B, and C are defined below. Find the probabilities for parts (a) through (h) below and express your results in words. Compute the conditional probabilities directly; do not use the conditional probability rule. Note that the ace has the highest value. A event a face card is selected B event a queen is selected C event a heart is selected
1) The probability that a queen is selected is 1/13 2) The probability that a queen is selected, given that a face card is selected is 1/3 3)The probability that a queen is selected, given that a heart is selected is 1/13. 4)The probability that a queen is selected, given that a face card is not selected is 0 5) The probability the face card is selected is 3/13 6) The probability that a face card is selected, given that a queen is selected is 1 7)The probability that a face card is selected given that a heart is selected is 3/13. 8) The probability that a face card is selected given that a queen is not selected is 1/6
Based on the given information, decide whether or not the two events in question are independent or whether it is not possible to tell.P(C)=0.2, P(D)=0.4, and P(C & D)=0.08
1) The two events are independent because P(C&D)=P(C)•P(D).
Below is a joint probability distribution for the members of a state congress by legislative group and political party. The "other" category includes Independents and vacancies. REP. SEN. P(P1) Democrats-P1 0.381. 0.117. 0.498 Republicans-P2 0.409. 0.086 0.495 Other-P3 0.003 0.004 0.007 P(CJ) 0.793 0.207 1.000
1). 0.498 2)0.793 3) 0.381 4) Use the special multiplication rule to determine whether events P1 and C1 are independent.? - NO
Information on the weights and years of experience for a football team was obtained. The given contingency table provides a cross-classification of those data. Compute the following conditional probabilities directly; that is, do not use the conditional probability rule. A player on the football team is selected at random. Complete parts (a) through (e) below. weight Y1 Y2 Y3 Y4 TOTAL -200 5 3. 1. 0. 9 200-300 8. 12. 15. 6. 41 +300 . 0 9. 7 0. 16 TOTAL. 13. 24. 23. 6. 66
1)0.197 2) 0.136 3) 0.556 4) 0.385 5) 19.7 6) 13.6 7) 55.6 8) 38.5
Suppose that A and B are two events. a. What does it mean for event B to be independent of event A? b. If event A and event B are independent, how can their joint probability be obtained from their marginal probabilities?
1)Event B is said to be independent of event A if P(B | A)=P(B). 2) the joint probability equals the product of the marginal probabilities; that is, P(A & B)=P(A)•P(B).
Decide whether or not the two events are independent or whether it is not possible to tell. Justify your answer. P(A)=16, P(B)=47, and P(A&B)=15
A and B are not independent because P(A&B)≠P(A)•P(B)
Suppose that C and D are two events such that P(C)=45 and P(C & D)=12. What is P(D|C)?
ANSWER- PDC 5/8
According to a research corporation, 38% of women in a particular region suffer from holiday depression, and, from a population report, 54% of adults in this region are women. Find the probability that a randomly selected adult in this region is a woman who suffers from holiday depression. Interpret your answer in terms of percentages.
The probability is 0.205 This means that 20.52 of all adults in this region are women who suffer from holiday depression
According to a research corporation, 47% of women in a particular region suffer from holiday depression, and, from a population report, 52% of adults in this region are women. Find the probability that a randomly selected adult in this region is a woman who suffers from holiday depression.
The probability is 0.2444.This means that 24.44% of all adults in this region are women who suffer from holiday depression.
