Probability Test

Result

Probability Test - 35

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

A random variable $$X$$ has the probability distribution:
$$X$$:
1
2
3
4
5
6
7
8
$$P(X)$$:
0.15
0.23
0.12
0.10
0.20
0.08
0.07
0.05
For the events $$E = \{X$$ is a prime number$$\}$$ and $$F = \{X < 4\}$$, the probability $$P(E \cup F)$$ is

A
$$0.35$$

B
$$0.77$$

C
$$0.87$$

D
$$0.50$$

Solution

$$P(E \cup F) = P(E) + P(F) -P(E\cap F)$$
$$= (0.23+0.12+0.2+0.07)+(0.15+0.23+0.12)-(0.23+0.12)\\ =0.62 + 0.15\\ = 0.77$$
Question 2
1 / -0

What is the probability that a number selected from the numbers 1, 2, 3, 4, 5......,16 is a prime number ?

A
$$\displaystyle \frac{1}{16}$$

B
$$\displaystyle \frac{5}{8}$$

C
$$\displaystyle \frac{3}{8}$$

D
$$\displaystyle \frac{7}{16}$$

Solution

Since, Total outcomes $$= 16$$
prime no's from $$1$$ to $$16$$ are: $$ 2,3,5,7,11,13 $$
total prime no's $$= 6$$
$$\therefore $$ favorable outcomes$$= 6$$
$$\therefore $$ probability = $$\dfrac {6}{16} = \dfrac 38 $$
$$\therefore $$ Option C is correct.
Question 3
1 / -0

Let A be a set containing n elements. A subset P of the set A is chosen at random.The set A is reconstructed by replacing the elements of $$P$$ and another subset $$Q$$ of A is chosen at random. The probability that $$ P \cap Q$$ contains exactly $$ m(m < n) $$ elements is

A
$$\dfrac{3^{n.m}}{4^{n}}$$

B
$$\dfrac{^{n}C_{m} \times 3^{m}}{4^{n}}$$

C
$$\dfrac{^{n}C_{m} \times 3^{n.m}}{4^{n}}$$

D
None of these

Solution

Let A be a set containing $$n$$ elements.
The number of way in which a subset $$A$$ cab be chosen
$$={{^nC_0}+{^nC_1}+{^nC_2}+......+{^nC_n}=2^n}$$
The set $$A$$ is reconstructed by replacing the elements of $$P$$ and another subset $$Q$$ of $$A=2^n+2^n=4^n$$
Probability that $$P\cap Q$$ contains exactly $$m$$ elements $$={^nC_m}$$
$$\therefore \dfrac{{^nC_m}\times3^{n.m}}{4^n}$$
Hence, the answer is $$ \dfrac{{^nC_m}\times3^{n.m}}{4^n}.$$
Question 4
1 / -0

If $$E$$ and $$F$$ be events in a sample space such that $$\displaystyle P(E\cup F)=0.8,P(E\cap F)=0.3$$ and $$P(E) = 0.5$$, then $$P (F)$$ is

A
$$0.6$$

B
$$1$$

C
$$0.8$$

D
None

Solution

Given, $$ P(E\cup F)=0.8,P(E\cup F)=0.3 $$ and $$ P(E) = 0.5 $$
Since, $$ P(E\cup F) = P(E) + P(F) - P(E\cap F) $$
$$\Rightarrow 0.8 = 0.5 + P(F) - 0.3 $$
$$\Rightarrow 0.8 = 0.2 + P(F) $$
$$\Rightarrow P(F) = 0.6 $$
$$\therefore $$ Option A is correct.
Question 5
1 / -0

In figure points A, B, C and D are the centre of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded region?

A
$$ \displaystyle \left (1 - \frac{ \pi}{4} \right )$$

B
$$ \displaystyle \left (1 - \frac{ \pi}{2} \right )$$

C
$$ \displaystyle \left (1 - \frac{ \pi}{6} \right )$$

D
$$ \displaystyle \left (2 - \frac{ \pi}{4} \right )$$

Solution

Side of a square $$= 2$$ unit.
Area of square $$= (2)^2$$ sq. unit $$= 4$$ sq. unit
Area of shaded region $$=$$ Area of a square $$-$$ Area of circle
$$=4- 4 \times \frac{1}{4} \pi (1)^2 = 4 - \pi$$
$$P $$(point chosen from shaded region) $$= \displaystyle \frac{4 - \pi}{4}$$
$$= \displaystyle \left (1 - \frac{ \pi}{4} \right )$$
Question 6
1 / -0

In a survey of $$45$$ houses, it was found that $$25$$ have cars and $$30$$ have two-wheelers. How many have both?

A
$$7$$

B
$$10$$

C
$$12$$

D
$$15$$

Solution

$$n(A\cup B)=n(A)+n(B)-n(A\cap B)$$
$$45=25+30-n(A\cap B)\implies n(A\cap B)=10$$
Question 7
1 / -0

Which of the following statements is true?

A
$$(A\cup B)^\prime=A\cap B$$

B
$$(A\cup B)^\prime=A^\prime\cap B$$

C
$$(A\cup B)^\prime=A\cap B^\prime$$

D
$$(A\cup B)^\prime=A^\prime\cap B^\prime$$

Solution

De Morgan's laws.
Question 8
1 / -0

If $$P\left ( A/B \right )=0.2$$ and $$P\left ( B \right )=0.5$$ and $$P\left ( A \right )=0.3.$$ Find $$P\left ( A\cap \bar{B} \right ).$$

A
$$0.1$$

B
$$0.9$$

C
$$0.8$$

D
$$0.2$$

Solution
Question 9
1 / -0

In a class of $$50$$ boys, $$35$$ like horror movies, $$30$$ like war movies and $$5$$ like neither. Find the number of those that like both.

A
$$20$$

B
$$25$$

C
$$15$$

D
$$28$$

Solution

45=35+30−n(A∩B)orn(A∩B)=20
Question 10
1 / -0

Let A, B, C be three events such that P (A) = 0.3 P(B) = 0.4, P(C) = 0.8, P(A $$\cap$$ B) = 0.08, P(A $$\cap$$ C) = 0.28, P(A $$\cap$$ B $$\cap$$ C) = 0.09. If P(A $$\cup$$ B $$\cup$$ C) $$\geq $$ 0.75, then

A
$$0.23 \leq P (B \cap C) \leq 0.48$$

B
$$0.23 \leq P (B \cap C) \leq 0.75$$

C
$$0.48 \leq P (B \cap C) \leq 0.75$$

D
None of these

Solution

Since $$P (A \cup B \cup C) \geq 0.75$$, therefore $$0.75 \leq P (A \cup B \cup C) \leq 1$$
$$\Rightarrow 0.75 \leq P(A) + P (B) + P(C) - P (A \cap B) - P (B \cap C) - P (A \cap C) + P (A \cap B \cap C) \leq 1$$
$$\Rightarrow 0.75 \leq 0.3 + 0.4 + 0.8 - 0.08 - P (B \cap C) -0.28 + 0.09 \leq 1$$
$$\Rightarrow 0.75 \leq 1.23 - p (B \cap C) \leq 1$$
$$\Rightarrow -0.48 \leq P (B \cap C) \leq - 0.23$$
$$\Rightarrow 0.23 \leq P (B \cap C) \leq 0.48$$.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

$$X$$:	1	2	3	4	5	6	7	8
$$P(X)$$:	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

Probability Test - 35

Result

Probability Test - 35

Score

-

Rank

-

SHARING IS CARING

Question 1

$$0.35$$

$$0.77$$

$$0.87$$

$$0.50$$

Solution

Question 2

$$\displaystyle \frac{1}{16}$$

$$\displaystyle \frac{5}{8}$$

$$\displaystyle \frac{3}{8}$$

$$\displaystyle \frac{7}{16}$$

Solution

Question 3

$$\dfrac{3^{n.m}}{4^{n}}$$

$$\dfrac{^{n}C_{m} \times 3^{m}}{4^{n}}$$

$$\dfrac{^{n}C_{m} \times 3^{n.m}}{4^{n}}$$

None of these

Solution

Question 4

$$0.6$$

$$1$$

$$0.8$$

None

Solution

Question 5

$$ \displaystyle \left (1 - \frac{ \pi}{4} \right )$$

$$ \displaystyle \left (1 - \frac{ \pi}{2} \right )$$

$$ \displaystyle \left (1 - \frac{ \pi}{6} \right )$$

$$ \displaystyle \left (2 - \frac{ \pi}{4} \right )$$

Solution

Question 6

$$7$$

$$10$$

$$12$$

$$15$$

Solution

Question 7

$$(A\cup B)^\prime=A\cap B$$

$$(A\cup B)^\prime=A^\prime\cap B$$

$$(A\cup B)^\prime=A\cap B^\prime$$

$$(A\cup B)^\prime=A^\prime\cap B^\prime$$

Solution

Question 8

$$0.1$$

$$0.9$$

$$0.8$$

$$0.2$$

Solution

Question 9

$$20$$

$$25$$

$$15$$

$$28$$

Solution

Question 10

$$0.23 \leq P (B \cap C) \leq 0.48$$

$$0.23 \leq P (B \cap C) \leq 0.75$$

$$0.48 \leq P (B \cap C) \leq 0.75$$

None of these

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.