Probability Test

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Probability Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

A die is thrown. Let $$A$$ be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then $$P(A \cup B)$$ is

A
$$1$$

B
$$\dfrac{2}{5}$$

C
$$\dfrac{3}{5}$$

D
$$0$$

Solution

We have
$$P(A) = \cfrac{3}{6} = \cfrac{1}{2}$$
$$P(B) = \cfrac{4}{6} = \cfrac{2}{3}$$
$$P(A\cap B) =$$ Probability of getting $$4=\cfrac{1}{6}$$
$$P(A \cup B) = P(A) + P(B) - P(A \cap B) = \cfrac{1}{2}+\cfrac{2}{3}-\cfrac{1}{6}=1$$
Question 2
1 / -0

To make a 750-piece jigsaw puzzle more challenging, a puzzle company includes 5 extra pieces of box along with the 750 pieces, and those 5 extra pieces do not fit anywhere in the puzzle. If Ramesh selects one piece at random from such a box, what is his probability of selecting the extra piece?

A
$$\displaystyle \frac { 1 }{ 5 } $$

B
$$\displaystyle \frac { 1 }{ 755 } $$

C
$$\displaystyle \frac { 1 }{ 750 } $$

D
$$\displaystyle \frac { 5 }{ 755 } $$

E
$$\displaystyle \frac { 5 }{ 750 } $$

Solution

Total no. of possible outcomes$$=750+5=755$$
Out of 755 possible outcomes there are 5 favorable outcomes ,since the box contain 5 extra pieces.
$$\therefore $$ Probability$$ =\dfrac{\text{favorable outcomes} }{\text{Total no. of possible outcomes}}=\dfrac{5}{755}$$
Question 3
1 / -0

There are $$20$$ marbles in a bag and $$10$$ of them are blue. What is the probability that any $$1$$ marble drawn at random will not be blue?

A
$$\dfrac{2}{5}$$

B
$$\dfrac{10}{9}$$

C
$$\dfrac{1}{20}$$

D
$$\dfrac{1}{2}$$

Solution

Out of $$20$$ marbles $$10$$ of them are blue.
Using complement, we know that
$$P$$ (Not getting the blue marble) $$=$$ $$1-\dfrac{10}{20}=\dfrac{1}{2}$$
Question 4
1 / -0

If $$\phi$$ represents an impossible event, then $$P(\phi) =$$ ?

A
$$0$$

B
$$1$$

C
$$\phi$$

D
$$-1$$

Solution

If $$\phi$$ represents an impossible event, then $$P(\phi)= 0$$
Because an impossible event is an event that will never occur in an experiment.
Question 5
1 / -0

An event in which all the possible outcomes of the experiments are present is known as ______ event.

A
a complement.

B
an experiment.

C
a sample space.

D
an exhaustive event.

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

Probability of getting a prime (or) composite is ________.

A
Mutually exclusive

B
Likely

C
$$0$$

D
None

Solution

Since if prime occur composite can never occur and vice versa.
So both events occurring of prime number and composite number are mutually exclusive.
Option $$A$$ is correct.
Question 7
1 / -0

Karishma and Reshma are playing Chess. The probability of Karishma winning is $$0.59$$. Then probability of Reshma winning the match is:

A
$$1$$

B
$$0.46$$

C
$$0.5$$

D
$$0.41$$

Solution

Let the probability of Karishma winning be given by $$k$$ and probability of Reshma winning be given by $$r$$.

As the two probabilities are mutually exhaustive $$k + r =1$$

From question $$k=0.59$$ so, $$r= 1- 0.59 $$

Therefore $$r= 0.41$$
Question 8
1 / -0

"The occurrence of one event excludes the occurrence of another event". In a random experiment of probability theory, it is called

A
Complementray event

B
Impossible event

C
Mutually exclusive event

D
Certain event

Solution

"The occurrence of one event excludes the occurrence of the other event."
In a random experiment of probability theory, this means that the occurence of one event does not affect the occurrence of another. Hence, they are called mutually exclusive events.
Therefore, $$C$$ is the correct option.
Question 9
1 / -0

If three events $$A$$, $$B$$, $$C$$ are mutually exclusive, then which one of the following is correct?

A
$$P\left( A\cup B\cup C \right) =0$$

B
$$P\left( A\cup B\cup C \right) =1$$

C
$$P\left( A\cap B\cap C \right) =0$$

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

Solution

Three events $$A.B.C$$ are mutually exclusive if they are disjoint or cannot be true at the same time.
Thus, the events are mutually exclusive if $$A\cap B\cap C=\phi$$
Thus, $$P(A\cap B\cap C)=0$$
Hence, C is correct.
Question 10
1 / -0

The probability of winning a game is $$\cfrac{5}{6}$$. Then the probability of losing it is.

A
$$-\cfrac{5}{6}$$

B
$$\cfrac{5}{6}$$

C
$$-\cfrac{1}{6}$$

D
$$\cfrac{1}{6}$$

Solution

Let $$P(W)$$ be the event of winning a game and $$P(L)$$ be the losing it.
Given that:
$$P(W)=\cfrac56$$
To find:
$$P(L)=?$$
Solution:
$$P(L)=1-P(W)$$
$$=1-\cfrac56$$
$$=\cfrac16$$
Therefore, D is the correct option.

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Re-Attempt Weekly Quiz Competition

Probability Test - 18

Result

Probability Test - 18

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SHARING IS CARING

Question 1

$$1$$

$$\dfrac{2}{5}$$

$$\dfrac{3}{5}$$

$$0$$

Solution

Question 2

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

$$\displaystyle \frac { 1 }{ 755 } $$

$$\displaystyle \frac { 1 }{ 750 } $$

$$\displaystyle \frac { 5 }{ 755 } $$

$$\displaystyle \frac { 5 }{ 750 } $$

Solution

Question 3

$$\dfrac{2}{5}$$

$$\dfrac{10}{9}$$

$$\dfrac{1}{20}$$

$$\dfrac{1}{2}$$

Solution

Question 4

$$0$$

$$1$$

$$\phi$$

$$-1$$

Solution

Question 5

a complement.

an experiment.

a sample space.

an exhaustive event.

Solution

Question 6

Mutually exclusive

Likely

$$0$$

None

Solution

Question 7

$$1$$

$$0.46$$

$$0.5$$

$$0.41$$

Solution

Question 8

Complementray event

Impossible event

Mutually exclusive event

Certain event

Solution

Question 9

$$P\left( A\cup B\cup C \right) =0$$

$$P\left( A\cup B\cup C \right) =1$$

$$P\left( A\cap B\cap C \right) =0$$

$$P\left( A\cap B\cap C \right) =1$$

Solution

Question 10

$$-\cfrac{5}{6}$$

$$\cfrac{5}{6}$$

$$-\cfrac{1}{6}$$

$$\cfrac{1}{6}$$

Solution

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