Probability Test 3

Result

Probability Test 3

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Set of all possible outcomes is called

A
Event

B
Probability

C
Experiment

D
None of the these

Solution

Set of all possible outcomes is called sample space.
Question 2
1 / -0

Two events $$A$$ and $$B$$ will be independent, if

A
$$A$$ and $$B$$ are mutually exclusive

B
$$P\left( A\prime B\prime \right) =\left[ 1-P\left( A \right) \right] \left[ 1-P\left( B \right) \right] $$

C
$$P\left( A \right) =P\left( B \right) $$

D
$$P\left( A \right) +P\left( B \right) =1$$

Solution

Two events $$A$$ and $$B$$ are said to be independent, if $$P\left( AB \right) =P\left( A \right) \times P\left( B \right) $$
Consider the result given in alternative $$B$$.
$$P\left( A\prime B\prime \right) =\left[ 1-P\left( A \right) \right] \left[ 1-P\left( B \right) \right] $$
$$\Rightarrow P\left( A\prime \cap B\prime \right) =1-P\left( A \right) -P\left( B \right) +P\left( A \right) \cdot P\left( B \right) $$
$$\Rightarrow 1-P\left( A\cup B \right) =1-P\left( A \right) -P\left( B \right) +P\left( A \right) \cdot P\left( B \right) $$
$$\Rightarrow P\left( A\cup B \right) =P\left( A \right) +P\left( B \right) -P\left( A \right) \cdot P\left( B \right) $$
$$\Rightarrow P\left( A \right) +P\left( B \right) -P\left( AB \right) =P\left( A \right) +P\left( B \right) -P\left( A \right) \cdot P\left( B \right) $$
$$\Rightarrow P\left( AB \right) =P\left( A \right) \cdot P\left( B \right) $$
This implies that $$A$$ and $$B$$ are independent, if $$P\left( A\prime B\prime \right) =\left[ 1-P\left( A \right) \right] \left[ 1-P\left( B \right) \right] $$
Question 3
1 / -0

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

A
$$0$$

B
$$\displaystyle\frac { 1 }{ 3 } $$

C
$$\displaystyle\frac { 1 }{ 12 } $$

D
$$\displaystyle\frac { 1 }{ 36 } $$

Solution
Question 4
1 / -0

What is the sample space for choosing a letter from a set of vowel ?

A
$$\{a, b, c ........z\}$$

B
$$\{a, e, i, o, u\}$$

C
$$\{a, e, i, o\}$$

D
None of the these

Solution

A letter is choose from set of vowels i.e. $$\{a, e, i, o, u\}$$.
Question 5
1 / -0

Sample space is a set of ..... of an experiment.

A
All possible outcomes

B
Selected outcomes

C
Both

D
None of these

Solution

A sample space is usually denoted using set notation, and the possible outcomes are listed as elements in the set.
For example, if the experiment is tossing a coin, the sample space is typically the set {head, tail}, i.e all possible outcomes.
Question 6
1 / -0

Which of the following is NOT a random experiment ?

A
Rolling an unbiased dice

B
Tossing a fair coin

C
Drawing a card from a well shuffled pack of 52 card

D
None of these

Solution

Rolling an unbiased dice results in $$6$$ outcomes. All have equal probability of showing up.
Tossing a fair coin results in $$2$$ outcomes. Both have equal probabilities of showing up.
Drawing a card from from a well shuffled pack of $$52$$ cards can have $$52$$ outcomes in total with equal probabilities.
Hence, above all are example of random experiment.
Question 7
1 / -0

When the dice are thrown, the event $$E = {4}$$, then this event is called ____.

A
compound event

B
simple event

C
impossible event

D
complementary event

Solution

When the dice are thrown, the event $$E = {4}$$ then this event is called simple event.
If there be only one element of the sample space in the set representing an event, then this event is called a simple or elementary event.
Question 8
1 / -0

Which of the following is not a random experiment?

A
Tossing a coin

B
Rolling a dice

C
Choosing a card from a deck of 52 cards

D
Throw a stone from a roof of a building

Solution

When we will throw a stone from the roof it will fall down it is not a random experiment.
Question 9
1 / -0

The outcomes of a random experiment are called _____ connected with the experiment.

A
space

B
events

C
experiment

D
random

Solution

The outcomes of a random experiment are called events connected with the experiment.
Example: $$1, 2, 3, 4, 5, 6$$ are the outcomes of the random experiment of rolling a dice and hence are events connected with it.
Question 10
1 / -0

What is called one or more outcomes of an experiment?

A
Space

B
Experiment

C
Sample

D
Event

Solution

Event is called one or more outcomes of an experiment.
Example: rolling a dice, we get a possible outcomes as $$\{1, 2, 3, 4, 5, 6\}$$.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Probability Test 3

Result

Probability Test 3

Score

-

Rank

-

SHARING IS CARING

Question 1

Event

Probability

Experiment

None of the these

Solution

Question 2

$$A$$ and $$B$$ are mutually exclusive

$$P\left( A\prime B\prime \right) =\left[ 1-P\left( A \right) \right] \left[ 1-P\left( B \right) \right] $$

$$P\left( A \right) =P\left( B \right) $$

$$P\left( A \right) +P\left( B \right) =1$$

Solution

Question 3

$$0$$

$$\displaystyle\frac { 1 }{ 3 } $$

$$\displaystyle\frac { 1 }{ 12 } $$

$$\displaystyle\frac { 1 }{ 36 } $$

Solution

Question 4

$$\{a, b, c ........z\}$$

$$\{a, e, i, o, u\}$$

$$\{a, e, i, o\}$$

None of the these

Solution

Question 5

All possible outcomes

Selected outcomes

Both

None of these

Solution

Question 6

Rolling an unbiased dice

Tossing a fair coin

Drawing a card from a well shuffled pack of 52 card

None of these

Solution

Question 7

compound event

simple event

impossible event

complementary event

Solution

Question 8

Tossing a coin

Rolling a dice

Choosing a card from a deck of 52 cards

Throw a stone from a roof of a building

Solution

Question 9

space

events

experiment

random

Solution

Question 10

Space

Experiment

Sample

Event

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.