MAT271 - Practice Exercise lii Question Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl. (ii) at least one is a girl. Question 2 A die is thrown 7 times. What is the chance that an odd number turns up up (i) exactly 4 times (ii) at least 4 times Question 3 How many times must a person toss a fair coin so that the probability of having at least one head is more than 90%. Question 4 In an entrance test, there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student knows the answer to the question is 90%. If he gets correct answer to a question, then find the probability that he was guessing? Question 5 A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. Find the probability that 5 comes before 7? Question 6 If A and B are two independent events such that P(AB)=2/15 and P (AB)=1/16. Find (i) P(A) and P(B) probabilities (ii) P(AUB) Question 7 A speaks truth in 60% cases and B speaks truth in 70% cases. Find the probability that they will say same thing while describing a single event? Question 8 A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick children in that neighborhood are sick with the flu, denoted by F, while 10% are sick with the measles, denoted by M. A well-known symptoms of measles is a rash, denoted by R. The probability of having a rash for a child sick with the measles is 0.95. However, occasionally children with the flu also develop a rash, with conditional probability 0.08. Upon examination the child, the doctor finds a rash. Then what is the probability that the child has the measles?
MAT271 - Practice Exercise lii Question Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl. (ii) at least one is a girl. Question 2 A die is thrown 7 times. What is the chance that an odd number turns up up (i) exactly 4 times (ii) at least 4 times Question 3 How many times must a person toss a fair coin so that the probability of having at least one head is more than 90%. Question 4 In an entrance test, there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student knows the answer to the question is 90%. If he gets correct answer to a question, then find the probability that he was guessing? Question 5 A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. Find the probability that 5 comes before 7? Question 6 If A and B are two independent events such that P(AB)=2/15 and P (AB)=1/16. Find (i) P(A) and P(B) probabilities (ii) P(AUB) Question 7 A speaks truth in 60% cases and B speaks truth in 70% cases. Find the probability that they will say same thing while describing a single event? Question 8 A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick children in that neighborhood are sick with the flu, denoted by F, while 10% are sick with the measles, denoted by M. A well-known symptoms of measles is a rash, denoted by R. The probability of having a rash for a child sick with the measles is 0.95. However, occasionally children with the flu also develop a rash, with conditional probability 0.08. Upon examination the child, the doctor finds a rash. Then what is the probability that the child has the measles?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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Transcribed Image Text:MAT271 - Practice Exercise lii
Question
Assume that each born child is equally likely to be a boy or a girl. If a family has two children,
what is the conditional probability that both are girls given that
(i) the youngest is a girl.
(ii) at least one is a girl.
Question 2
A die is thrown 7 times. What is the chance that an odd number turns up up
(i) exactly 4 times
(ii) at least 4 times
Question 3
How many times must a person toss a fair coin so that the probability of having at least one head
is more than 90%.
Question 4
In an entrance test, there are multiple choice questions. There are four possible answers to each
question, of which one is correct. The probability that a student knows the answer to the question
is 90%. If he gets correct answer to a question, then find the probability that he was guessing?
Question 5
A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. Find the
probability that 5 comes before 7?
Question 6
If A and B are two independent events such that P(AB)=2/15 and P (AB)=1/16. Find
(i) P(A) and P(B)
probabilities
(ii) P(AUB)
Question 7
A speaks truth in 60% cases and B speaks truth in 70% cases. Find the probability that they will
say same thing while describing a single event?
Question 8
A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick
children in that neighborhood are sick with the flu, denoted by F, while 10% are sick with the
measles, denoted by M. A well-known symptoms of measles is a rash, denoted by R. The
probability of having a rash for a child sick with the measles is 0.95. However, occasionally
children with the flu also develop a rash, with conditional probability 0.08. Upon examination
the child, the doctor finds a rash. Then what is the probability that the child has the measles?
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