Simple and Compound Event

Q. A student appears for tests $I,II$ and $III$. The student is successful only if he passes either in tests $I$ and $II$ or tests $I$ and $III$(not all the $3$).
The probabilities of the student passing in tests $I,II,III$ are $p,q$ and $\frac{1}{3}$ respectively. The probability that the student is successful is $\frac{1}{6}$ and the relation between $p$ and $q$ is $\frac{1}{k}=pq+p$. Then the value of $k$ is:

Q.

Which of the following is/are simple event?

1. While throwing a die an even prime number turns up

2. While throwing a die, an even or odd number turns up

3. In a football match, a draw happens. (when we are considering results of that match)

4. Two heads occur while throwing a coin twice

Q. Which of the following is/are compound events?

1. An event which has more than one sample point

2. An event combined with another event

3. An event derived from another event

4. An event where compound interest happen

Q. Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”. C denote the event “three tails show” and D denote the event ‘a head shows on the first coin”. Which events are (i) mutually exclusive? (ii) simple? (iii) compound?

Q. A box contains $6$ green balls, $4$ blue balls and $5$ yellow balls. A ball is drawn at random. Find the probability of
(a) Getting a yellow ball.
(b) Not getting a green ball.

1. $\frac{4}{15},\frac{3}{15}$
2. $\frac{1}{5},\frac{1}{3}$
3. $\frac{2}{3},\frac{1}{15}$
4. $\frac{1}{3},\frac{3}{5}$

Q. A coin is tossed two times, what is the probability of getting head at least once.

Q. A bag contains cards which are numbered from $2$ to $90$. A card is drawn at random from the bag. Find the probability that it bears
(i) a two digit number (ii) a number which is a perfect square

Q. Sita and Geta are friends, what is the probability that both will have different birthdays (ignoring a leap year)

1. $\frac{1}{365}$
2. $\frac{1}{364}$
3. $\frac{364}{365}$
4. None of these

Q. Calculate the probability that a number selected at random from the set {$2,3,7,12,15,22,72,108$} will be divisible by both $2$ and $3$.

1. $\frac{1}{4}$
2. $\frac{3}{8}$
3. $\frac{3}{5}$
4. $\frac{5}{8}$
5. $\frac{7}{8}$

Q. Two dice are tossed once. The probability of getting an even number at the first die or a total of $8$ is

1. $\frac{1}{36}$
2. $\frac{3}{36}$
3. $\frac{11}{36}$
4. $\frac{20}{36}$