Probability Test 19

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Probability Test 19

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Weekly Quiz Competition

Question 1
1 / -0

Given that $$A \subset B$$, then identify the correct statement

A
$$P(A/B) = P(A)$$

B
$$P (A/B) \le P(A)$$

C
$$P(A/B) \ge P(A)$$

D
$$P(A/B) = P(A) - P(B)$$

Solution

$$A \subset B$$
$$P (A/B) = \dfrac{P(A \cap B)}{P (B)} = \dfrac{P (A)}{P(B)} \neq P(A)$$ (always)
$$P(A/B) = \dfrac{P(A)}{P(B)} \ge P(A)$$
Question 2
1 / -0

The number of committees formed by taking $$5men$$ and $$5women$$ from $$6women$$ and $$7men$$ are

A
252

B
125

C
126

D
64

Solution
Question 3
1 / -0

Probability of hitting a target independently of $$4$$ persons are $$\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}, \dfrac{1}{8}$$. Then the probability that target is hit, is?

A
$$\dfrac{1}{192}$$

B
$$\dfrac{5}{192}$$

C
$$\dfrac{25}{32}$$

D
$$\dfrac{7}{32}$$

Solution

$$P(H)=1-P$$(Not Hitting)
$$=1-\dfrac{1}{2}\cdot \dfrac{2}{3}\cdot \dfrac{3}{4}\cdot \dfrac{7}{8}=\dfrac{25}{32}$$.
Question 4
1 / -0

The probability of happening of an event A is $$0.5$$ and that of B is $$0.3$$. If A and B are mutually exclusive events, then the probability of neither A nor B is?

A
$$0.4$$

B
$$0.5$$

C
$$0.2$$

D
$$0.9$$

Solution

$$P(A)=0.5$$; $$P(B)=0.3$$

$$\therefore P(\bar{A}\cap\bar{B})=1-P(A\cup B)=1-[P(A)+P(B)]$$ $$[\because\ P(A\cap B)=\phi $$ as they are mutually exclusive events $$]$$

$$=1-[0.5+0.3]$$

$$=0.2$$
Question 5
1 / -0

If $$6P(A)=8P(B)=14P(A\cap B)=1$$, then $$P\left( \cfrac { A' }{ B } \right) =........$$

A
$$\cfrac { 3 }{ 7 } $$

B
$$\cfrac { 4 }{ 7 } $$

C
$$\cfrac { 3 }{ 5 } $$

D
$$\cfrac { 2 }{ 5 } $$

Solution

we know that
$$P(A)= \dfrac16$$ $$P(B)=\dfrac18$$ $$P(A\cap B)=\dfrac1{14}$$
by using conditional probability
$$P\left( \cfrac { \overline { A } }{ B } \right) =\cfrac { P(\overline { A } \cap B) }{ P(B) }$$
$$ =\cfrac { P(B)-P( { A } \cap B) }{ P(B) }$$
$$ =1-\cfrac { \cfrac { 1 }{ 14 } }{ \cfrac { 1 }{ 8 } }$$
$$ =\cfrac { 3 }{ 7 } $$
Question 6
1 / -0

Given two mutually exclusive events $$A$$ and $$B$$ such that $$P(A)=\dfrac 12$$ and $$P(B)=\dfrac 13$$, find $$P(A\ or\ B)$$

A
$$\dfrac{3}{5}$$

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

C
$$\dfrac{4}{5}$$

D
None of these

Solution

Given mutually exclusive events
$$\Rightarrow \ A\cap B=\phi$$
$$\therefore \ P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
$$\Rightarrow \ P(A\cup B)=\dfrac {1}{2}+\dfrac {1}{3}-0$$
$$\Rightarrow \ P(A\cup B)=\dfrac {3+2}{6}$$
$$\Rightarrow \ P(A\ or\ B)=P(A\cup B)=\dfrac {5}{6}$$
Question 7
1 / -0

From a well shuffled deck of $$52$$ cards, $$4$$ cards are drawn at random. What is the probability that all the drawn cards are of the same colour.

A
$$\dfrac{184}{833}$$

B
$$\dfrac{92}{833}$$

C
$$\dfrac{92}{2466}$$

D
$$\dfrac{46}{833}$$

Solution
Question 8
1 / -0

If $$A$$ and$$B$$ are mutually exclusive events such that $$P(A)=0.4,P(B)=x$$ and $$P(A\cup B)=0.5$$, then $$x=$$?

A
$$0.2$$

B
$$0.1$$

C
$$\cfrac{4}{5}$$

D
none of these

Solution
Question 9
1 / -0

Let $$S$$ and $$T$$ are two events defined on a sample space with probabilities $$P(S)=0.5,P(T)=0.69,P(S/T)=0.5$$ Event $$S$$ and $$T$$ are

A
mutually exculsive

B
independent

C
mutually exclusive and independent

D
neither mutually exclusive nor independent

Solution

Given, $$S$$ and $$T$$ are two events defined on a sample space with probabilities
$$P(S)=0.5,P(T)=0.69,P(S/T)=0.5$$
$$P(S/T)=\dfrac{P(S \cap T)}{P(T)}$$
$$\Rightarrow 0.5=\dfrac{P(S \cap T)}{0.69}$$
$$\Rightarrow P(S \cap T)=0.5 \times 0.69=P(S)P(T)$$
Therefore, $$S$$ and $$T$$ are independent.

$$\therefore P(S \cap T)=P(S)P(T)$$
$$=0.69\times 0.5=0.345$$
As intersection is not zero $$S$$ and $$ T$$ are not mutually exclusive.
Option B is correct.
Question 10
1 / -0

In a random experiment,it the occurrence of one event prevents the occurrence of other event,is

A
A complementary event

B
a certain event

C
Not mutually exclusive event

D
mutually exclusive event

Solution

In a random experiment if the occurrence of one event prevents the occurrence of other event it is mutually exclusive.

Explanation:

As we know

The two events both of which can not occur at the same time i.e one event prevent the occurrence of the other i.e their intersection is null are called mutually exclusive events.

Hence, In a random experiment if the occurrence of one event prevents the occurrence of other event it is mutually exclusive.

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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

$$P(A/B) = P(A)$$

$$P (A/B) \le P(A)$$

$$P(A/B) \ge P(A)$$

$$P(A/B) = P(A) - P(B)$$

Solution

Question 2

252

125

126

64

Solution

Question 3

$$\dfrac{1}{192}$$

$$\dfrac{5}{192}$$

$$\dfrac{25}{32}$$

$$\dfrac{7}{32}$$

Solution

Question 4

$$0.4$$

$$0.5$$

$$0.2$$

$$0.9$$

Solution

Question 5

$$\cfrac { 3 }{ 7 } $$

$$\cfrac { 4 }{ 7 } $$

$$\cfrac { 3 }{ 5 } $$

$$\cfrac { 2 }{ 5 } $$

Solution

Question 6

$$\dfrac{3}{5}$$

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

$$\dfrac{4}{5}$$

None of these

Solution

Question 7

$$\dfrac{184}{833}$$

$$\dfrac{92}{833}$$

$$\dfrac{92}{2466}$$

$$\dfrac{46}{833}$$

Solution

Question 8

$$0.2$$

$$0.1$$

$$\cfrac{4}{5}$$

none of these

Solution

Question 9

mutually exculsive

independent

mutually exclusive and independent

neither mutually exclusive nor independent

Solution

Question 10

A complementary event

a certain event

Not mutually exclusive event

mutually exclusive event

Solution

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