Multiplication Rule

Q.

Five coins whose faces are marked $2,3$ are tossed. The chance of obtaining a total of $12$ is

1. $\frac{1}{32}$

2. $\frac{1}{16}$

3. $\frac{3}{16}$

4. $\frac{5}{16}$

Q.

The probability that when a hand of 7 cards is dealt from a well-shuffled deck of 52 cards, it contains at least 3 king is:

1. 

2. 

3. 

4. 

Q. A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.

Q. Three cards are drawn successively, without replacement from a pack of 52 well-shuffled cards. What is the probability that the third card drawn is a queen given that first card is king of spades while second card is an ace?

1. $\frac{2}{16575}$
2. $\frac{3}{66300}$
3. $\frac{1}{16575}$
4. $\frac{2}{16575}$

Q. Cards of an ordinary deck of playing cards are placed into two heaps. Heap-l consists of all the red cards and heap-ll consists of all the black cards. A heap is chosen at random and a card is drawn, the probability that the card drawn is a king, is

Q. If two different numbers are taken from the set {0, 1, 2, 3, .... 10}, then the probability that their sum as well as absolute difference are both multiple of 4, is ?

1. $\frac{6}{55}$
2. $\frac{12}{55}$
3. $\frac{14}{45}$
4. $\frac{7}{55}$

Q.

An article manufactured by a company consists of two parts $X$ and $Y$. In the process of manufacture of the part $X$, $9$ out of $100$ parts may be defective. Similarly, $5$ out of $100$ are likely to be defective in the manufacture of part $Y$. Calculate the probability that the assembled product will not be defective.

1. $0.6485$

2. $0.6565$

3. $0.8645$

4. None of these

Q. Miss $X$ takes either tea or coffee at morning break. If she had tea one morning, the probability that she has tea the next morning is $\mathrm{0.4.}$ If she had coffee one morning, the probability that she has coffee the next morning is $\mathrm{0.3.}$ Suppose she has coffee on a Monday morning. The probability that she has tea on the following Wednesday morning, is

1. $0.46$
2. $0.49$
3. $0.51$
4. $0.61$

Q. A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Q.

Four fair dice $D_1,D_2,D_{3}and{D}_4$ each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1,D_{2}and{D}_3$, is ?

1. $\frac{91}{216}$

2. $\frac{108}{216}$

3. $\frac{125}{216}$

4. $\frac{127}{216}$

Q. The Boolean expression $\sim (p\Rightarrow (\sim q\left)\right)$ is equivalent to

1. $(\sim p)\Rightarrow q$
2. $p\vee q$
3. $q\Rightarrow \sim p$
4. $p\wedge q$

Q. Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the two numbers is less than 4, is

1. $\frac{1}{15}$
2. $\frac{14}{15}$
3. $\frac{1}{5}$
4. $\frac{4}{5}$

Q. In an objective paper, there are two sections of $10$ questions each. For "section $1$", each question has $5$ options and only one option is correct and "section $2$" has $4$ options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in "section $1$" is $1$ and in "section $2$" is $3.$
(There is no negative marking)
If a canidate attempts only two questions by guessing, one from "section $1$" and one from "section $2$", the probability that he scores in both questions is

1. $\frac{74}{75}$
2. $\frac{1}{25}$
3. $\frac{1}{15}$
4. $\frac{1}{75}$

Q. An ordinary die has four blank faces. One face marked $2$, an other marked $3$. Then the probability of obtaining a total of exactly $12$ in $5$ throws is

1. $\frac{15}{6^4}$
2. $\frac{10}{6^4}$
3. $\frac{5}{6^4}$
4. $\frac{6}{6^4}$

Q. From a deck of 52 cards, four cards are drawn simultaneously, find the chance that they will be the four honours of the same suit.

Q. In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i) the student opted for NCC or NSS.
(ii) the student has opted neither NCC nor NSS.
(iii) the student has opted NSS but not NCC.

Q. One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be
(1). diamond card
(2). not an ace
(3). a club card
(4). not a black card