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 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 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?

$A$ person is known to speak the truth in $3$ out of $4$ occasions. If he throws a die and reports that it is six,then the probability that it is actually six is

Let $n_1$ and $n_2$ be the number of red and black balls,respectively,in box $I$. Let $n_3$ and $n_4$ be the number of red and black balls,respectively,in box $II$.
$1.$ One of the two boxes,box $I$ and box $II$,was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box $II$ is $\frac{1}{3}$,then the correct option$(s)$ with the possible values of $n_1, n_2, n_3$ and $n_4$ is(are):
$(A)$ $n_1=3, n_2=3, n_3=5, n_4=15$
$(B)$ $n_1=3, n_2=6, n_3=10, n_4=50$
$(C)$ $n_1=8, n_2=6, n_3=5, n_4=20$
$(D)$ $n_1=6, n_2=12, n_3=5, n_4=20$
$2.$ $A$ ball is drawn at random from box $I$ and transferred to box $II$. If the probability of drawing a red ball from box $I$,after this transfer,is $\frac{1}{3}$,then the correct option$(s)$ with the possible values of $n_1$ and $n_2$ is(are):
$(A)$ $n_1=4, n_2=6$
$(B)$ $n_1=2, n_2=3$
$(C)$ $n_1=10, n_2=20$
$(D)$ $n_1=3, n_2=6$
Give the answer for question $1$ and $2$.

$A$ man is known to speak the truth $7$ out of $10$ times. After throwing a die with $100$ faces marked $1, 2, 3, \dots, 100$,the man reports that he got a prime number. What is the probability that it is actually a prime number?

$A$ pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade is: