$A$ survey of people in a given region showed that $20 \%$ were smokers. The probability of death due to 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 lung cancer in the region is $0.006$, what is the probability of death due to lung cancer given that a person is a smoker?
- A$1 / 140$
- B$1 / 70$
- C$3 / 140$
- D$1 / 10$
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$A$ man is known to speak truth $3$ out of $4$ times. He throws a die and reports that it is a six. Find the probability that it is actually a six.
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View SolutionThree companies $C_1, C_2, C_3$ produce car tyres. $A$ car manufacturing company buys $40 \%$ of its requirement from $C_1, 35 \%$ from $C_2$ and $25 \%$ from $C_3$. The company knows that $2 \%$ of the tyres supplied by $C_1, 3 \%$ by $C_2$ and $4 \%$ by $C_3$ are defective. If a tyre chosen at random from the consignment received is found defective, then the probability that it was supplied by $C_2$ is:
There are two boxes, each containing $10$ balls. In each box, some are black and the rest are white. $A$ ball is drawn at random from one of the boxes and it is found to be black. If the probability that the black ball drawn is from the second box is $\frac{1}{5}$, then the number of black balls in the first box is:
The following table shows the probability of selecting the boxes $A, B$ and $C$ and the number of balls of different colours contained in them. If a ball is selected at random and it is found to be green,what is the probability that it was selected from box $C$?
Box White Green Red Probability $A$ $1$ $2$ $3$ $\frac{1}{2}$ $B$ $2$ $3$ $1$ $\frac{1}{3}$ $C$ $3$ $1$ $2$ $\frac{1}{6}$
| Box | White | Green | Red | Probability |
|---|---|---|---|---|
| $A$ | $1$ | $2$ | $3$ | $\frac{1}{2}$ |
| $B$ | $2$ | $3$ | $1$ | $\frac{1}{3}$ |
| $C$ | $3$ | $1$ | $2$ | $\frac{1}{6}$ |
$A$ student has to write the words $ABILITY$, $PROBABILITY$, $FACILITY$, $MOBILITY$. He wrote one word and erased all the letters in it except two consecutive letters. If '$LI$' is left after erasing, then the probability that the boy wrote the word $PROBABILITY$ is
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