Probability Test

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Probability Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

If $$P(C)=\cfrac { 2 }{ 7 } $$, then $$P(\overline { C } )=$$.......................

A
$$\cfrac { 5 }{ 7 } $$

B
$$\cfrac { 2 }{ 7 } $$

C
$$0$$

D
$$1$$

Solution

Given $$P(C)=\cfrac { 2 }{ 7 } $$
We know that $$P(C)+P(\overline { C } )=1$$
$$\implies P(\overline { C } )=1-P(C)=1-\cfrac { 2 }{ 7 } =\cfrac { 5 }{ 7 } $$
Hence, the answer is $$\dfrac{5}{7}$$.
Question 2
1 / -0

Consider the following statements:
1. If $$A$$ and $$B$$ are exhaustive events, then their union is the sample space.
2. If $$A$$ and $$B$$ are exhaustive events, then their intersection must be an empty event.
Which of the above statements is/are correct?

A
1 only

B
2 only

C
Both 1 and 2

D
Neither 1 nor 2

Solution

Exhaustive events are those events, whose union covers the whole sample space. The probability of occurring at least one of them is $$1$$. So, their intersection may or may not be empty.
Hence, A is correct.
Question 3
1 / -0

Which one of the following is correct?

A
An event having no sample point is called an elementary event

B
An event having one sample point is called an elementary event

C
An event having two sample point is called an elementary event

D
An event having many sample point is called an elementary event

Solution

An elementary event is an event which contains only a single element in the sample space. So, it will have only $$1$$ sample point.
Hence, option B is true
Question 4
1 / -0

The probability of compliment event of impossible event is ..................

A
0.5

B
0

C
1

D
0.46

Solution

Let $$E$$ be an event which is impossible.
That is, $$E$$ does not occur ever. So, there will be no elements in $$E$$
Thus, the probability of $$E$$ will be zero.
So, the probability of an impossible event is zero.
$$\therefore$$ The probability of compliment event of impossible event $$=$$ Total probability $$-$$ Probability of $$E=1 - 0 = 1$$
Hence, the answer is $$1$$.
Question 5
1 / -0

If the probability of winning a game is $$0.3$$, then what is the probability of losing it?

A
$$0.1$$

B
$$0.3$$

C
$$0.7$$

D
$$1.3$$

Solution

Let $$A$$ be an event of winning and $$B$$ be an event of losing the game.
Given $$P(A)=0.3$$
Total probability $$=P(A)+P(B)$$
$$\Rightarrow$$ $$1=0.3+P(B)$$
$$\Rightarrow$$ $$P(B)=1-0.3=0.7$$
$$\therefore$$ $$P(B)=0.7$$
Question 6
1 / -0

Two cards are drawn from a single deck of $$52$$ cards one after the other. Find the probability of selecting a king from the first card and queen from the second card.

A
$$\dfrac{1}{26}$$

B
$$\dfrac{4}{52}$$

C
$$\dfrac{16}{663}$$

D
$$\dfrac{4}{663}$$

Solution

Probability of selecting a king in the first card is $$\dfrac{4}{52}$$. (Since $$4$$ kings in $$52$$ cards).
Probability of selecting a queen from the second card after the first card is drawn out is $$\dfrac{4}{51}$$. (Since $$4$$ queens in left over $$51$$ cards.
Now probability of selecting a king from the first card and queen from the second card is $$\dfrac{4}{52}\times \dfrac{4}{51}=\dfrac{4}{663}$$.
Hence, option D is correct.
Question 7
1 / -0

If $$P(A) = 1$$, then the event $$A$$ is known as

A
Symmetric event

B
Dependent event

C
Improbable event

D
Sure event

Solution

The probability is the possibility of an event happening when the probability of an event is 1, it means the event will occur for sure.
Question 8
1 / -0

If $$P(A) = 0$$, then the event $$A$$

A
Will never happen

B
Will always happen

C
May happen

D
May not happen

Solution

The probability is the possibility of happening of an event.
If the probability of an event is zero, it means the event is an impossible event and it will never occur.
Question 9
1 / -0

Toss three fair coins simultaneously and record the outcomes. Find the probability of getting atmost one head in the three tosses.

A
$$\dfrac{1}{6}$$

B
$$\dfrac{1}{4}$$

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

D
$$\dfrac{1}{3}$$

Solution

Toss three fair coins simultaneously and record the outcomes.The sample space is HHH, HHT, HTH, HTT, THH, THT, TTH and TTT N=8
atmost one head in 4 events
the probability of getting atmost one head in the three tosses.$$P(E)=\dfrac{4}{8}=\dfrac{1}{2}$$
Question 10
1 / -0

A fair dice has faces numbered $$0, 1, 7, 3, 5$$ and $$9$$. If it is thrown, the probability of getting an odd number is:

A
$$1$$

B
$$\dfrac {2}{3}$$

C
$$\dfrac {5}{6}$$

D
$$\dfrac {1}{6}$$

Solution

A fair dice has faces numbered as $$0,1,7,3,5,9$$
Since $$1, 3, 5,7, 9$$ are odd numbers.
Number of favorable outcomes $$= 5$$
Total number of possible outcomes $$= 6$$
So, the probability of getting an odd number $$P(E)$$ $$=$$ $$\dfrac {\text{Favourable outcomes}}{\text{Total number of possible outcomes}}$$ $$=$$ $$\dfrac {5}{6}$$

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Re-Attempt Weekly Quiz Competition

Probability Test - 19

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Probability Test - 19

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SHARING IS CARING

Question 1

$$\cfrac { 5 }{ 7 } $$

$$\cfrac { 2 }{ 7 } $$

$$0$$

$$1$$

Solution

Question 2

1 only

2 only

Both 1 and 2

Neither 1 nor 2

Solution

Question 3

An event having no sample point is called an elementary event

An event having one sample point is called an elementary event

An event having two sample point is called an elementary event

An event having many sample point is called an elementary event

Solution

Question 4

0.5

0

1

0.46

Solution

Question 5

$$0.1$$

$$0.3$$

$$0.7$$

$$1.3$$

Solution

Question 6

$$\dfrac{1}{26}$$

$$\dfrac{4}{52}$$

$$\dfrac{16}{663}$$

$$\dfrac{4}{663}$$

Solution

Question 7

Symmetric event

Dependent event

Improbable event

Sure event

Solution

Question 8

Will never happen

Will always happen

May happen

May not happen

Solution

Question 9

$$\dfrac{1}{6}$$

$$\dfrac{1}{4}$$

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

$$\dfrac{1}{3}$$

Solution

Question 10

$$1$$

$$\dfrac {2}{3}$$

$$\dfrac {5}{6}$$

$$\dfrac {1}{6}$$

Solution

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