Probability Test

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Probability Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

There are $$30$$ tickets numbered from $$1$$ to $$30$$ in a box . A ticket is drawn at random. What is the probability that the ticket drawn bears an odd number?

A
$$\displaystyle \frac{1}{2}$$

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

C
$$\displaystyle \frac{2}{3}$$

D
$$\displaystyle \frac{1}{4}$$

Solution

Total number of outcomes $$= 30$$
Favourable outcomes (odd number on the ticket) $$= 15$$
Probability $$=\dfrac{15}{30} = \dfrac{1}{2}$$
Question 2
1 / -0

The probability of an impossible event is ____

A
$$3$$

B
$$2$$

C
$$1$$

D
$$0$$

Solution

Probability of event in $$E$$, $$ P\left( E \right) =\dfrac { \text {number of events in E} }{ \text {Total number of possible events}} $$
If the desirable event does not happen even once, then the numerator in the above formula becomes equal to zero.
Question 3
1 / -0

Suppose six coins are flipped. Then the probability of getting at least one tail is:

A
$$\dfrac {71}{72}$$

B
$$\dfrac {53}{54}$$

C
$$\dfrac {63}{64}$$

D
$$\dfrac {1}{12}$$

Solution

Total number of events that would occur by flipping six coins
$$=2^6=64.$$
Probability that no tail occurs $$=\dfrac {1}{64}$$
Probability of occurring at least one tail$$=1-\dfrac {1}{64}=\dfrac {63}{64}$$
Question 4
1 / -0

In tossing a coin, the chance of throwing head and tail alternatively in $$3$$ successive trials is

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

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

C
$$\dfrac{1}{5}$$

D
$$\dfrac{1}{48}$$

Solution

Favourable outcomes $$= \{HTH,THT\}= 2$$ outcomes
Total number of outcomes $$= 8$$
Probability $$=$$ $$\dfrac{2}{8}$$ $$=$$ $$\dfrac{1}{4}$$
Question 5
1 / -0

A die is thrown then find the probability of getting an odd number.

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

B
$$\displaystyle \frac{2}{3}$$

C
$$\displaystyle \frac{1}{2}$$

D
None of these.

Solution

Sample space $$= {1,2,3,4,5,6}$$
odd nos. $$= 1,3,5$$
probability of getting odd nos.$$=\cfrac{3}{6}$$ $$=\cfrac{1}{2}$$
Question 6
1 / -0

If $$P(A) = P(B)$$, then the two events $$A$$ and $$B$$ are -

A
Independent

B
Dependent

C
Equally likely

D
Both (A) and (C)

Solution

Events are said to be equally likely if there is no preference for a particular event over the other.

Examples

When a coin is tossed, Head (H) or Tail is equally likely to occur.
If $$P(A)=P(B),$$ then the two events A and B are equally likely
Question 7
1 / -0

If the events $$A$$ and $$B$$ be mutually exclusive, then $$P(A+B)$$ will be equal to

A
$$\displaystyle P\left ( A \right )+P\left ( B \right )$$

B
$$\displaystyle P\left ( A \right )-P\left ( B \right )$$

C
$$\displaystyle P\left ( A \right ).P\left ( B \right )$$

D
$$\displaystyle P\left ( A \right )/P\left ( B \right ).$$

Solution

For mutually exclusive events A and B, we have
$$\displaystyle A\cap B= \phi $$ so that $$\displaystyle P\left ( A\cap B \right )= 0.$$ So in this case, we have
$$\displaystyle P\left ( A\cup B \right )$$ or $$\displaystyle P\left ( A+B \right )= P\left ( A \right )+P\left ( B \right ).$$
Question 8
1 / -0

If two coins are tossed then find the probability of the event that at least one tail turns up is:

A
$$\displaystyle \frac{1}{4}$$

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

C
$$\displaystyle \frac{1}{2}$$

D
$$\displaystyle \frac{3}{4}$$

Solution

2 coins tossed sample space $$= {(h,h),(h,t),(t,h),(t,t)}$$
Number of outcomes that have atleast one tail $$= 3 $$
probability is $$\cfrac{ 3}{4}$$
Question 9
1 / -0

All possible outcomes of a random experiment forms the -

A
Events

B
Sample space

C
Both

D
None of these

Solution

Sample Space is the set of all possible outcomes of an experiment. It is denoted by S.
Examples:
When a coin is tossed, S = {H, T} where H = Head and T = Tail
When a dice is thrown, S = {1, 2 , 3, 4, 5, 6}
When two coins are tossed, S = {HH, HT, TH, TT} where H = Head and T = Tail
Question 10
1 / -0

The sum of the probabilities of all the elementary events of an experiment is ____?

A
$$4$$

B
$$3$$

C
$$2$$

D
$$1$$

Solution

The probability $$p$$ of any event must be greater than or equal to $$0$$.
In other words, $$0 \leq p \leq 1$$.
Since $$1$$ is the maximum limit, all probabilities must add to $$1$$.
Hence, the sum of the probabilities of all the elementary events of an experiment is $$1$$.

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Probability Test - 10

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Probability Test - 10

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Question 1

$$\displaystyle \frac{1}{2}$$

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

$$\displaystyle \frac{2}{3}$$

$$\displaystyle \frac{1}{4}$$

Solution

Question 2

$$3$$

$$2$$

$$1$$

$$0$$

Solution

Question 3

$$\dfrac {71}{72}$$

$$\dfrac {53}{54}$$

$$\dfrac {63}{64}$$

$$\dfrac {1}{12}$$

Solution

Question 4

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

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

$$\dfrac{1}{5}$$

$$\dfrac{1}{48}$$

Solution

Question 5

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

$$\displaystyle \frac{2}{3}$$

$$\displaystyle \frac{1}{2}$$

None of these.

Solution

Question 6

Independent

Dependent

Equally likely

Both (A) and (C)

Solution

Question 7

$$\displaystyle P\left ( A \right )+P\left ( B \right )$$

$$\displaystyle P\left ( A \right )-P\left ( B \right )$$

$$\displaystyle P\left ( A \right ).P\left ( B \right )$$

$$\displaystyle P\left ( A \right )/P\left ( B \right ).$$

Solution

Question 8

$$\displaystyle \frac{1}{4}$$

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

$$\displaystyle \frac{1}{2}$$

$$\displaystyle \frac{3}{4}$$

Solution

Question 9

Events

Sample space

Both

None of these

Solution

Question 10

$$4$$

$$3$$

$$2$$

$$1$$

Solution

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