Probability Test

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Probability Test - 50

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Weekly Quiz Competition

Question 1
1 / -0

If A & B are two events such that $$p(A)\neq 0$$ & $$ P(B)\neq 1,t hen\ P(A'/B)$$

A
$$1-P(A/B)$$

B
$$1-P(B/A)$$

C
$$1-P(AUB)/P(B)$$

D
$$P(A)/P(B)$$

Solution

$$P(A'/B)=1-P(A/B)=1-P(A\cap B)/P(B)$$
Question 2
1 / -0

If A and B are two events, such that P(A or B)=P(A), then

A
events A and B are mutually exclusive

B
events A and B are statistically independent

C
event B is a subset of event A

D
event A is a subset of event B

Solution

$$P\left( AorB \right) =P\left( A\cup B \right) =P\left( A \right) $$
In venn diagram it is shown that $$B$$ is a part of $$A$$ Hence probability of occurrance of event $$A$$ or event $$B$$ will be $$P(A)$$.
$$\therefore B$$ is subset of $$A$$
Question 3
1 / -0

A and B are two independent events such that $${ P\left( { A }^{ ' }\cap B \right) =\dfrac { 2 }{ 15 } }$$then P(B) is equal to :

A
$$\frac { 4 }{ 5 } $$

B
$$\frac { 1 }{ 6 } $$

C
$$\frac { 1 }{ 5 } $$

D
$$\frac { 5 }{ 6 } $$

Solution
Question 4
1 / -0

The probability of the sun setting in the west is..............

A
1.5

B
0.5

C
0

D
1

Solution
Question 5
1 / -0

Let A and B be two events such that $$P(A) =7/20, P(B) = 9/20, P(A\cup B)=11/20$$ ,then the value of $$P(\bar{A}\cup B)$$ is equal to

A
$$1/4$$

B
$$1/5$$

C
$$1/10$$

D
$$9/10$$

Solution

From given, we have,

$$P(A\cup B)=\dfrac{11}{20}$$

$$P(A)=\dfrac{7}{20}$$

Now, we use formula,

$$P(\bar{A}\cup B)=P(A\cup B)+P(A)$$

$$=\dfrac{11}{20}+\dfrac{7}{20}$$

$$=\dfrac{9}{10}$$
Question 6
1 / -0

If truth value of $$p$$ is $$T$$ , $$q$$ is $$F$$ , then truth values of $$( p \rightarrow q )$$ and $$( q \rightarrow p ) \vee ( \sim p )$$ are respectively N/A

A
$$F , F$$

B
$$F , T$$

C
$$T , F$$

D
$$T , T$$
Solution
- Truth table
  p q $$(p \to q)$$ $${ \sim p}$$ $$ \sim p \vee q$$
  $${q \to p}$$ $$q \to p \vee \sim p$$
  T F F F F T T
  $$\begin{matrix} p=T \\ q=F \\ \\ then \\ (p\to q)\, \, \, and\, \, \left( { q\to p } \right) \vee \left( { \sim p } \right) \, \, \\ is\, \, false \\ \\ \end{matrix}$$
Question 7
1 / -0

If A and B are such events that $$P(A)>0$$ and $$ P(B)\neq 1$$ then $$P\left(\dfrac{\bar{A}}{\bar{B}}\right)$$ is equal to-

A
$$1-P\left(\dfrac{A}{B}\right)$$

B
$$1-P\left(\dfrac{\bar{A}}{B}\right)$$

C
$$\dfrac{1-P(A\cup B)}{P(\bar{B})}$$

D
$$None$$

Solution
Question 8
1 / -0

A card is drawn from a well shuffled pack of 52 cards. Events A and B are defined as follows :
A : Getting a card of spade
B : Getting an ace, then A and B are .....

A
mutually exclusive and independent events

B
not mutually exclusive but independent events

C
mutually exclusive and not independent events

D
neither mutually exclusive nor independent events

Solution

A: Getting a card of spade

B : Getting an ace

i) Events A & B are not mutually exclusive

since the occurrence of one doesn't rule out the occurrence of others. For instance, getting an ace of spade

ii) Events A & B are independent as occurrence

of one is not dependent on other.

also $$P(A\cap B)=\dfrac {1}{52}$$ since ther is only $$1$$ ace of spades

& $$P(A)P(B)=\dfrac{13}{52}\times \dfrac{4}{52}= \dfrac{1}{52}$$

$$P(A\cap B)=P(A)P(B)\Rightarrow $$ Independent events

$$\Rightarrow $$ A & B are not mutually exclusive

but independent.
Question 9
1 / -0

4 normal distinguishable dice are rolled once. The number of possible outcomes in which at least one dice shows up 2?

A
216

B
648

C
625

D
671

Solution

The number of possible outcomes in which atleast one dice shows up $$2$$ is:
$$\begin{array}{l} =(6\times 6\times 6\times 6)-(5\times 5\times \times 5\times 5) \\= 1296-625=671 \end{array}$$

Hence, the correct option is $$D$$
Question 10
1 / -0

$$8$$ players compete in a tournament, every one plays everyone else just once. The winner of a game gets $$1$$, the loser $$0$$ or each gets $$\dfrac{1}{2}$$ if the game is drawn. The final result is that every one gets a different score and the player playing placing second gets the same as the total of four bottom players.The total score of all the players is

A
$$28$$

B
$$21$$

C
$$20$$

D
$$22$$

Solution

The players get $$1$$ for winning
and $$\dfrac 12$$ for a draw
So the sum of points of the players for one match is $$1$$
Hence the total score for $$^8C_2=\dfrac{8\times7}2$$ matches is $$28$$
'

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Re-Attempt Weekly Quiz Competition

p	q	$$(p \to q)$$	$${ \sim p}$$	$$ \sim p \vee q$$	$${q \to p}$$	$$q \to p \vee \sim p$$
T	F	F	F	F	T	T

Probability Test - 50

Result

Probability Test - 50

Score

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Rank

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SHARING IS CARING

Question 1

$$1-P(A/B)$$

$$1-P(B/A)$$

$$1-P(AUB)/P(B)$$

$$P(A)/P(B)$$

Solution

Question 2

events A and B are mutually exclusive

events A and B are statistically independent

event B is a subset of event A

event A is a subset of event B

Solution

Question 3

$$\frac { 4 }{ 5 } $$

$$\frac { 1 }{ 6 } $$

$$\frac { 1 }{ 5 } $$

$$\frac { 5 }{ 6 } $$

Solution

Question 4

1.5

0.5

0

1

Solution

Question 5

$$1/4$$

$$1/5$$

$$1/10$$

$$9/10$$

Solution

Question 6

$$F , F$$

$$F , T$$

$$T , F$$

$$T , T$$

Solution

Question 7

$$1-P\left(\dfrac{A}{B}\right)$$

$$1-P\left(\dfrac{\bar{A}}{B}\right)$$

$$\dfrac{1-P(A\cup B)}{P(\bar{B})}$$

$$None$$

Solution

Question 8

mutually exclusive and independent events

not mutually exclusive but independent events

mutually exclusive and not independent events

neither mutually exclusive nor independent events

Solution

Question 9

216

648

625

671

Solution

Question 10

$$28$$

$$21$$

$$20$$

$$22$$

Solution

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