Independent events

Q.

If a dice is thrown twice, then the probability of getting $1$ in the first throw only is

1. $\frac{1}{36}$

2. $\frac{3}{36}$

3. $\frac{5}{36}$

4. $\frac{1}{6}$

Q.

Cards are drawn one by one without replacement from a pack of $52$ cards. The probability that $10$ cards will precede the first ace is

1. $\frac{241}{1456}$

2. $\frac{164}{4165}$

3. $\frac{451}{884}$

4. None of these

Q. A box contains 4 blue, 5 green and 4 yellow balls. Two balls are drawn with replacement. Find the probability that the first ball is blue and the second ball is yellow.

1. $\frac{1}{13}$
2. $\frac{16}{169}$
3. $\frac{20}{169}$
4. $\frac{4}{13}$

Q.

Let $B_i(i=1,2,3)$ be three independent events in a sample space. The probability that only $B_1$occur is $\alpha$, only $B_2$ occurs is $\beta$ and only $B_2$ occurs is $\gamma$. Let $p$ be the probability that none of the events $B_i$ occurs and these $4$ probabilities satisfy the equations $\left(\alpha –2\beta \right)p=\alpha \beta$ and $\left(\beta –3\gamma \right)p=2\beta \gamma$(All the probabilities are assumed to lie in the interval $\left(0,1\right)$. Then $\frac{P\left(B_1\right)}{P\left(B_3\right)}$is equal to __________.

Q.

Two cards are drawn at random from a standard deck of $52$ cards. What is the probability that both cards are aces?

Q. A real estate man has eight master keys to open several new homes. Only one master key will open any given home. If 40% of these homes are usually left unlocked, the probability that the real estate man can get into a specific home, if it is given that he selected 3 keys randomly before leaving his office, is equal to:

1. $\frac{5}{8}$
2. $\frac{3}{8}$
3. $\frac{3}{4}$
4. $\frac{9}{40}$

Q.

The probability that $\mathrm{A}$speaks the truth is $\frac{4}{5}$. A coin is tossed. A report that a head appears. The probability that actually there was a head $?$

Q. An ordinary cubical die has four blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 12 in 5 throws is

1. $\frac{5}{2529}$
2. $\frac{5}{1264}$
3. $\frac{5}{1296}$
4. $\frac{5}{1944}$

Q. A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the
$\left(1\right)$ Yellow ball
$\left(2\right)$ Red ball
$\left(3\right)$ Blue ball?

1. $\left(1\right)\frac{1}{2}\left(2\right)\frac{1}{3}\left(3\right)\frac{1}{2}$
2. $\left(1\right)\frac{1}{3}\left(2\right)\frac{1}{2}\left(3\right)\frac{1}{3}$
3. $\left(1\right)\frac{1}{3}\left(2\right)\frac{1}{3}\left(3\right)\frac{1}{3}$
4. $\left(1\right)\frac{1}{2}\left(2\right)\frac{1}{2}\left(3\right)\frac{1}{2}$

Q. The probability that the ${13}^{th}$ day of a randomly chosen month is a Friday, is

1. $\frac{1}{12}$
2. $\frac{2}{3}$
3. $\frac{1}{84}$
4. $None$

Q. A bag contains 3 white, 3 black and 2 red balls. One by one, three balls are drawn without replacing them. The probability that the third ball is red, is given by:

1. $\frac{1}{12}$
2. $None$
3. $\frac{1}{4}$
4. $\frac{5}{25}$

Q. A bag contains 6 red and 4 blue balls (all are different). A fair die is rolled and number of balls equals to that appearing on the die is chosen from the bag at random. The probability that all the balls selected are red is

1. $\frac{127}{630}$
2. $\frac{1}{5}$
3. $\frac{1}{30}$
4. $\frac{1}{6}$

Q. From a bag containing 9 distinct white and 9 distinct black, 9 balls are drawn at random one by one, the drawn balls being replaced each time. The probability that at least four balls of each colour is in the draw, is

1. A little less than $\frac{1}{2}$
2. a little greater than $\frac{1}{2}$
3. $\frac{1}{2}$
4. $\frac{1}{3}$

Q.

A and B are two mutually exclusive and exhaustive events with $\mathrm{P}\left(\mathrm{B}\right)=3\mathrm{P}\left(\mathrm{A}\right).$ What is the value of $P\left(\overline{B}\right)$

1. $\frac{3}{4}$

2. $\frac{1}{4}$

3. $\frac{1}{3}$

4. $\frac{2}{3}$