Probability Tes...

The probability that certain electronic component fails when first used is $$0.10.$$ If it does not fail immediately, the probability that is lasts for one year is $$0.99.$$ The probability that a new component will last for one year is

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

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

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

For $$k=1, 2, 3$$ the box $${ B }_{ k }$$ contains $$k$$ red balls and $$\left( k+1 \right) $$ white balls, let $$P\left( { B }_{ 1 } \right) =\dfrac { 1 }{ 2 } ,P\left( { B }_{ 2 } \right) =1$$ and $$P\left( { B }_{ 3 } \right) =\dfrac { 1 }{ 6 } $$. 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 $${ B }_{ 2 }$$ is

A student answers a multiple choice question with $$5$$ alternatives, of which exactly one is correct. The probability that he knows the correct answer is $$p, 0 < p < 1$$. 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

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 $$9/10$$. If he gets the correct answer to a question, then the probability that he was guessing is

A survey of people in a given region showed that $$20 \%$$ were smokers. The probability of death due lung cancer, given that a person smoked, was $$10$$ 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 $$0.006$$. What is the probability of depth due to lung cancer given that a person is a smoker?

Suppose a girl throws a die. If she gets a $$5$$ or $$6$$, she tosses a coin $$3$$ times and notes the number of heads. If she gets $$1, 2, 3$$ or $$4$$ 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 $$1, 2, 3$$ or $$4$$ with the die?

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