1.In a recent study, the following data was obtained in response tothe question,
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Question
1.In a recent study, the following data was obtained in response tothe question, “Do you favor recycling in yourneighborhood?” Males Females Yes 53 51 No 55 45 No Opinion 8 9 If a person is picked at random, what is the probability thatthe person is either male or has no opinion regarding recycling?Round your answer to the nearest hundred. 2. You are dealt one card from a standard 52-card deck. Findthe probability of being dealt neither a jack nor a queen. Stateyour answer in the form of a reduced fraction using the sign "/" asthe divisor sign. 3.Given that P(A or B) =1/3 P(A) = 1/4, and P(A and B) = 1/9,find P(B). 4. If one card is drawn from a standard 52 card playing deck,determine the probability of getting a jack or a queen or aheart. 5.If two events A and B are mutuallyexclusive, then the probability that either A orBoccurs is equal to 6.A study of consumer smoking habits includes 153 people inthe 18-22 age bracket (41 of whom smoke), 123 people in the 23-30age bracket (32 of whom smoke), and 93 people in the 31-40 agebracket (24 of whom smoke). If one person is randomly selected fromthis sample, find the probability of getting someone who is age18-22 or does not smoke. 7.You are dealt one card from a standard 52-card deck. Findthe probability of being dealt neither a jack nor a queen. Stateyour answer in the form of a reduced fraction 8.Given that P(A or B) = 1/3 P(A) = 1/6, and P(A and B) =1/7, find P(B). 9.Consider an experiment in which two dice are rolled. Threeevents are definedA: The sum of the numbers on the two dice is 4.
B: The sum of the numbers on the two dice is 10.
C: Each of the two dice shows the same number.
10. If a person is picked at random, what is the probability thatthe person is either male or has no opinion regarding recycling?Round your answer to the nearest hundred. 2. You are dealt one card from a standard 52-card deck. Findthe probability of being dealt neither a jack nor a queen. Stateyour answer in the form of a reduced fraction using the sign "/" asthe divisor sign. 3.Given that P(A or B) =1/3 P(A) = 1/4, and P(A and B) = 1/9,find P(B). 4. If one card is drawn from a standard 52 card playing deck,determine the probability of getting a jack or a queen or aheart. 5.If two events A and B are mutuallyexclusive, then the probability that either A orBoccurs is equal to 6.A study of consumer smoking habits includes 153 people inthe 18-22 age bracket (41 of whom smoke), 123 people in the 23-30age bracket (32 of whom smoke), and 93 people in the 31-40 agebracket (24 of whom smoke). If one person is randomly selected fromthis sample, find the probability of getting someone who is age18-22 or does not smoke. 7.You are dealt one card from a standard 52-card deck. Findthe probability of being dealt neither a jack nor a queen. Stateyour answer in the form of a reduced fraction 8.Given that P(A or B) = 1/3 P(A) = 1/6, and P(A and B) =1/7, find P(B). 9.Consider an experiment in which two dice are rolled. Threeevents are defined
A: The sum of the numbers on the two dice is 4.
B: The sum of the numbers on the two dice is 10.
C: Each of the two dice shows the same number.
10. Males Females Yes 53 51 No 55 45 No Opinion 8 9
Explanation / Answer
2. no. of cards in a deck of 52 leaving behind jacks andqueens = 52 - 4- 4 = 44the probability of being dealt neither a jack nor a queen= 44/52 =0.85
3.Given that P(A or B) =1/3 P(A) = 1/4, and P(A and B) = 1/9,find P(B).
P(A or B) = P(A) + P(B) - P(A and B)
hence, 1/3 = 1/4 +P(B) - 1/9
hence, P(B) = (1/3)-(1/4)+(1/9) = 0.11
4. probability of getting a jack P(J)= 4/52
probability of getting a queen P(Q)= 4/52
probability of getting a heart P(H)= 13/52
probability of getting a jack and queen P(J and Q) = 0
probability of getting a queen and heart P(Q and H) = 1/52
probability of getting a jack and heart P(J and H) = 1/52
probability of getting a jack and queen and heart P(J and Q and H)= 0
If one card is drawn from a standard 52 card playingdeck, the probability of getting a jack or a queen or a heart= P(J) + P(Q) + P(H) - P(J n Q) - P(Q n H) - P(J n H) + P(J n Q nH)
= (4+4+13-0-1-1+0)/52 = 0.37
5.If two events A and B are mutuallyexclusive, then the probability that either A orBoccurs is equal to P(A)+P(B)
6.A study of consumer smoking habits includes 153 people inthe 18-22 age bracket (41 of whom smoke), 123 people in the 23-30age bracket (32 of whom smoke), and 93 people in the 31-40 agebracket (24 of whom smoke).
total no. of people = 153+123+93 =369
no. of people who doesnt smoke = (153-41)+(123-32)+(93-24) =272
probability of selecting a person who doesnt smoke P(D)=272/369
probability of getting someone who is age 18-22 P(E)= 153/369
probability of getting someone who is age 18-22 and who doesntsmoke P(EnD) = (153-41)/369
=112/369
hence, the probability of getting someone who is age 18-22 or doesnot smoke.=P(E or D) = P(E)+P(D)-P(EnD)
= (153+272-112)/369 = 0.85
7.You are dealt one card from a standard 52-card deck.
the probability of being dealt neither a jack nor a queen =(52-4-4)/52 = 0.85
8.Given that P(A or B) = 1/3 P(A) = 1/6, and P(A and B) =1/7, find P(B).
P(A or B) = P(A) + P(B) - P(A and B)
hence, 1/3 = 1/6 +P(B) - 1/7
hence, P(B) = (1/3)-(1/6)+(1/7) = 0.31
9.Consider an experiment in which two dice are rolled. Threeevents are defined
total sample space when two dice are rolled = 6*6 = 36
A: The sum of the numbers on the two dice is 4.
sample space = {(2,2), (1,3), (3,1)}
hence probability of A = 3/36 = 0.083
B: The sum of the numbers on the two dice is 10.
sample space= {(5,5),(4,6),(6,4)}
hence probability of B = 3/36 = 0.083
C: Each of the two dice shows the same number.
sample space = {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}
hence probability of C = 6/36 = 0.17
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