Self Studies

Probability Tes...

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  • Question 1
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    The probability that certain electronic component fails when first used is 0.10.0.10. If it does not fail immediately, the probability that is lasts for one year is 0.99.0.99. The probability that a new component will last for one year is

  • Question 2
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    Directions For Questions

    A JEE aspirant estimates that she will be successful with an 8080 percent chance if she studies 1010 hours per day, with a 6060 percent chance if she studies 7 hours per day and with a 40 percent chance if she studies 4 hours per day. She further believes that she will study 10 hours, 7 hours and 4 hours per day with probabilities 0.1, 0.2 and 0.7, respectively.

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    Given that she does not achieve success, the chance she studied for 4 hour, is

  • Question 3
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    A signal which can be green or red with probability 45\displaystyle \frac{4}{5} and 15\displaystyle \frac{1}{5}, respectively, is received at station A and then transmitted to station B. The probability of each station receiving the signal correctly is 34\displaystyle \frac{3}{4}. If the signal received at station B is green, then the probability that the original signal was green is

  • Question 4
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    A person goes to office by car, scooter, bus and train, probability of which are 17,37,27\dfrac 17, \dfrac 37, \dfrac 27 and 17\dfrac 17, respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is 29,19.49\dfrac 29, \dfrac 19. \dfrac 49, and 19\dfrac 19, respectively. Given that he reached office in time, the probability that he travelled by a car, is

  • Question 5
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    For k=1,2,3k=1, 2, 3 the box Bk{ B }_{ k } contains kk red balls and (k+1)\left( k+1 \right) white balls, let P(B1)=12,P(B2)=1P\left( { B }_{ 1 } \right) =\dfrac { 1 }{ 2 } ,P\left( { B }_{ 2 } \right) =1 and P(B3)=16P\left( { B }_{ 3 } \right) =\dfrac { 1 }{ 6 } . A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box B2{ B }_{ 2 } is

  • Question 6
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    A student answers a multiple choice question with 55 alternatives, of which exactly one is correct. The probability that he knows the correct answer is p,0<p<1p, 0 < p < 1. If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is

  • Question 7
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    In an entrances test, there are multiple choice questions. There are four possible answers it each question, of which one is correct. The probability that a student knows the answer to a question is 9/109/10. If he gets the correct answer to a question, then the probability that he was guessing is

  • Question 8
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    A survey of people in a given region showed that 20%20 \% were smokers. The probability of death due lung cancer, given that a person smoked, was 1010 times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lungs cancer in the region is 0.0060.006. What is the probability of depth due to lung cancer given that a person is a smoker?

  • Question 9
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    Suppose a girl throws a die. If she gets a 55 or 66, she tosses a coin 33 times and notes the number of heads. If she gets 1,2,31, 2, 3 or 44 she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1,2,31, 2, 3 or 44 with the die?

  • Question 10
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    A screw factory has two machines, the M1, which is old, and does 75%75 \% of all the screws, and the M2, newer but small, that does 25%25 \% of the screws. The M1 does 4%4 \% of defective screws, while the M2 just does 2%2 \% of defective screws. If we choose a screw at random: what is the probability that it turns out to be defective?

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