Probability Test

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Probability Test - 14

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Weekly Quiz Competition

Question 1
1 / -0

The probability of a certain event is

A
$$0$$

B
$$1$$

C
greater than $$1$$

D
less than $$0$$

Solution

An event which always happens is called a sure event or a certain event. So the probability of a certain event is $$1$$.
For example, when we throw a die, then the event "getting a number less than $$7$$" is a certain event.
Question 2
1 / -0

If the probability of India winning a particular hockey match is $$0.81$$. What is the probability of India losing that match?

A
$$0.19$$

B
$$0.29$$

C
$$0.59$$

D
$$0.49$$

Solution

Let $$E$$ be the event of India winning
then $$\bar{E}$$ is the event of India not winning (losing)
$$P(\bar{E}) = 1 - P(E) = 1-0.81 = 0.19$$
Question 3
1 / -0

The probability of an impossible event is

A
$$1$$

B
$$0$$

C
less than $$0$$

D
greater than $$1$$

Solution

An event that has no chance of occurring is called an impossible event.
So, the probability of an impossible event is always zero.
Question 4
1 / -0

If P(E) = 0 then E is a/an

A
sure event

B
impossible event

C
equally likely event

D
none of these

Solution

$$P(E)=\dfrac{\text{number of outcomes favorable}}{\text{Total numbers of possible outcomes}}$$
If $$P(E)=0$$, then the event is called impossible event.
For example -
When a dice is thrown the possible outcomes are $$1,2,3,4,5$$ and $$6$$,
then the probability is to getting the number $$7$$ in a single throw of a dice is $$0$$, then this is called impossible event.
$$P(E)=\dfrac{0}{6}=0$$
Question 5
1 / -0

If $$U=\{1,2,3,4,5,6\}$$, $$P=\{1,4,6\}$$, $$Q=\{2,3,4,5\}$$, $$R=\{1,2,6\}$$, then the number of elements in the set $$(P\cap Q)^\prime$$ is

A
$$2$$

B
$$0$$

C
$$4$$

D
$$5$$

Solution

$$P\cap Q=\{4\}$$
$$(P\cap Q)^\prime=\{1,2,3,5,6\}$$
Question 6
1 / -0

If probability of getting a red ball from a bag containing blue and red balls is 0.52. then probability of getting a blue ball from the same bag is

A
0.52

B
0.42

C
0.48

D
0

Solution

If probability of getting a red ball from a bag containing blue and red balls $$=0.52$$

The probability of getting a blue ball from the same bag is
$$=1-0.52$$
$$0.48$$
Hence, this is the answer.
Question 7
1 / -0

In a class of $$30$$ students, $$10$$ take mathematics, $$15$$ take physics and $$10$$ take neither. The number of students who take both mathematics and physics is

A
$$15$$

B
$$5$$

C
$$3$$

D
$$2$$

Solution

$$n(A\cup B)=n(A)+n(B)-n(A\cap B)$$
$$20=10+15-n(A\cap B)\:or\:n(A\cap B)=5$$
Question 8
1 / -0

If P(E) = 0 Then P(not E) is

A
1

B
-1

C
0

D
1/2

Solution

We have,
$$P(E)=0$$

We know that
$$P(E)+P(notE)=1$$
$$0+P(notE)=1$$
$$P(notE)=1$$

Hence, this is the answer.
Question 9
1 / -0

Let $$A$$ and $$B$$ be two sets such that $$n(A)=70$$, $$n(B)=90$$, and $$n(A\cup B)=110$$. Then $$n(A\cap B)$$ equals

A
$$0$$

B
$$20$$

C
$$100$$

D
$$120$$

Solution

$$n(A\cup B)=n(A)+n(B)-n(A\cap B)$$
$$110=70+60-n(A\cap B)\implies n(A\cap B)=20$$
Question 10
1 / -0

Out of 35 students participating in a debate 10 are girls The probability that the winner is a boy will be

A
$$ \displaystyle \frac{3}{7} $$

B
$$ \displaystyle \frac{5}{7} $$

C
$$ \displaystyle \frac{1}{7} $$

D
$$ \displaystyle \frac{2}{7} $$

Solution

Total number of student=35
No. of girls=10
Then number of boys$$=35-10=25$$
The probability that the winner is a boy$$=\dfrac{25}{35}=\dfrac{5}{7}$$

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Re-Attempt Weekly Quiz Competition

Probability Test - 14

Result

Probability Test - 14

Score

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Rank

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SHARING IS CARING

Question 1

$$0$$

$$1$$

greater than $$1$$

less than $$0$$

Solution

Question 2

$$0.19$$

$$0.29$$

$$0.59$$

$$0.49$$

Solution

Question 3

$$1$$

$$0$$

less than $$0$$

greater than $$1$$

Solution

Question 4

sure event

impossible event

equally likely event

none of these

Solution

Question 5

$$2$$

$$0$$

$$4$$

$$5$$

Solution

Question 6

0.52

0.42

0.48

0

Solution

Question 7

$$15$$

$$5$$

$$3$$

$$2$$

Solution

Question 8

1

-1

0

1/2

Solution

Question 9

$$0$$

$$20$$

$$100$$

$$120$$

Solution

Question 10

$$ \displaystyle \frac{3}{7} $$

$$ \displaystyle \frac{5}{7} $$

$$ \displaystyle \frac{1}{7} $$

$$ \displaystyle \frac{2}{7} $$

Solution

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