Probability Test

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Probability Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

What is the sample space for choosing an odd number from $$2$$ to $$10$$ at random?

A
$${2, 4, 6, 8, 10}$$

B
$${1, 2, 3, 5}$$

C
$${3, 5, 7, 9}$$

D
$${1, 2, 3, 5, 7}$$

Solution

Sample space is the collection of all possible events.
So, the sample space for choosing an odd number from $$2$$ to $$10$$ at random $$=$$ $${3, 5, 7, 9}$$
Question 2
1 / -0

A glass jar contains $$10$$ red, $$12$$ green, $$14$$ blue and $$16$$ yellow marbles. If a single marble is chosen at random from the jar, find the sample space.

A
{red, green, blue, yellow}

B
{red, blue, yellow}

C
{red, yellow}

D
{red, green, blue}

Solution

Sample space is the collection of all possible outcomes.
So, sample space $$=$$ {red, green, blue, yellow}
Question 3
1 / -0

Find the sample space for choosing a prime number less than $$20$$ at random.

A
$${2, 3, 5, 7, 11, 13, 17, 19}$$

B
$${2, 3, 4, 5, 7, 11, 13, 17, 19}$$

C
$${ 2, 3, 5, 7, 11, 13, 17, 19, 20}$$

D
$${2, 3, 5, 7, 11, 13, 17, 19, 15}$$

Solution

Sample space is the collection of all possible events.
So, sample space for choosing a prime number less than $$20$$ $$= {2, 3, 5, 7, 11, 13, 17, 19}$$
Question 4
1 / -0

The set of all possible outcomes of any experiment is called

A
event

B
random experiment

C
sample space

D
sample point

Solution

The set of all possible outcomes of any experiment is called sample space.
Example: toss a coin
Sample space, $$S = \{H, T\}$$
$$H=$$ head
$$T=$$ tail
Question 5
1 / -0

Toss a fair coin $$3$$ times in a row, how many elements are in the sample space?

A
$$2$$

B
$$4$$

C
$$6$$

D
$$8$$

Solution

Sample space is the collection of all possible events.
So, sample space, $$S = {(H, H, H), (H, H, T), (H, T, T), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)}$$
Therefore, there are $$8$$ elements in sample space.
Question 6
1 / -0

A number from $$2$$ to $$13$$ is chosen at random. What is the probability that the number chosen is not even?

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

B
$$\dfrac{3}{4}$$

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

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

Solution

$$P$$ (getting odd number) $$=$$ $$\dfrac{6}{12}= \dfrac{1}{2}$$
$$P$$ (getting not an even number) $$= 1 - P$$ (getting odd number)$$=$$ $$1-\dfrac{1}{2} = \dfrac{1}{2}$$
Question 7
1 / -0

There are $$25$$ stones in a jar and $$15$$ of them are brown. If a stone is chosen, what is the probability that it is not brown?

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

B
$$\dfrac{10}{20}$$

C
$$\dfrac{15}{20}$$

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

Solution

From the problem,
Using complement, we know
$$P$$ (not getting the brown) $$=$$ $$1-\dfrac{15}{25}=\dfrac{2}{5}$$
Question 8
1 / -0

An event which will not occur on any account is called an

A
impossible event

B
sure event

C
exhaustive event

D
complementary

Solution

An event which will not occur on any account is called an impossible event.
Example: getting $$10$$ in rolling a die once is an impossible event.
Question 9
1 / -0

A fair die is thrown. What is the probability that the score is not a factor of $$5$$?

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

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

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

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

Solution

The numbers on the die that are factors of $$5$$ are $$1$$ and $$5$$.
$$P$$ (Score is a factor of $$5$$) $$=$$ $$\dfrac{2}{6} = \dfrac{1}{3}$$
$$P$$ (Score is not a factor of $$6$$) $$=$$ $$1-\dfrac{1}{3} = \dfrac{2}{3}$$
Question 10
1 / -0

Events $$E_1, E_2, ....E_n$$ are ______ events if their union is the sample space $$S$$.

A
complement

B
exhaustive

C
impossible event

D
sure event

Solution

When a sample space is distributed down into some mutually exclusive events such that their union forms the sample space itself, then such events are called exhaustive events.

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Probability Test - 17

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Probability Test - 17

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Question 1

$${2, 4, 6, 8, 10}$$

$${1, 2, 3, 5}$$

$${3, 5, 7, 9}$$

$${1, 2, 3, 5, 7}$$

Solution

Question 2

{red, green, blue, yellow}

{red, blue, yellow}

{red, yellow}

{red, green, blue}

Solution

Question 3

$${2, 3, 5, 7, 11, 13, 17, 19}$$

$${2, 3, 4, 5, 7, 11, 13, 17, 19}$$

$${ 2, 3, 5, 7, 11, 13, 17, 19, 20}$$

$${2, 3, 5, 7, 11, 13, 17, 19, 15}$$

Solution

Question 4

event

random experiment

sample space

sample point

Solution

Question 5

$$2$$

$$4$$

$$6$$

$$8$$

Solution

Question 6

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

$$\dfrac{3}{4}$$

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

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

Solution

Question 7

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

$$\dfrac{10}{20}$$

$$\dfrac{15}{20}$$

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

Solution

Question 8

impossible event

sure event

exhaustive event

complementary

Solution

Question 9

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

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

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

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

Solution

Question 10

complement

exhaustive

impossible event

sure event

Solution

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