Probability Test

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Probability Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

If for two events $$A$$ and $$B, P(A\cup B) = 1$$, then $$A$$ and $$B$$ are

A
Mutually exclusive events

B
Equally likely events

C
Exhaustive events

D
Dependent events

Solution

When atleast one of the events occur compulsorily from the list of events, then it is also known as exhaustive events. i.e., $$P(A\cup B)=1$$
Question 2
1 / -0

The probability that a man will be alive in $$40$$ years is $$\dfrac{3}{5}$$, and the probability that his wife will also survive $$40$$ years is $$\dfrac{2}{3}$$. Find the probability that both will be alive

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

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

C
$$\dfrac{2}{15}$$

D
$$\dfrac{6}{15}$$

Solution

Given the probability that a man will be alive in $$40$$ years is $$\dfrac 35$$
and, the probability that his wife will also survive $$40$$ years is $$\dfrac 23$$
Considering these two probabilities are independent. Hence, the probability that both will be alive is $$\dfrac 35\times \dfrac 23=\dfrac 25$$
Question 3
1 / -0

If $$P(A\cap B) = 0$$, then the two events $$A$$ and $$B$$ are

A
Mutually exclusive

B
Exhaustive

C
Equally likely

D
Independent

Solution

Mutually exclusive events cannot occur simultaneously. Formally said, the intersection of each two of them is empty (the null event): $$A ∩ B =$$ $$\phi$$. In consequence, mutually exclusive events have the property: $$P(A ∩ B) = 0$$.
Question 4
1 / -0

Identify and write the like terms in each of the following groups.
(i) $$ a^2, b^2, -2a^2 , c^2 , 4a$$

A
$$(a^6,2a^2)$$

B
$$(a^2,-2a^2)$$

C
$$(a^3,2a^2)$$

D
$$(a^2,2a^3)$$

Solution

In $$a^{2},b^{2},-2a^{2},c^{2},4a.$$
$$a^{2}$$ and $$-2a^{2}$$ are like terms because $$-2a^{2}$$ is a factor of $$a^{2}$$
$$B$$ is correct.
Question 5
1 / -0

$$A, B, C$$ are three mutually independent with probabilities $$0.3, 0.2$$ and $$0.4$$ respectively.
What is $$P(A \cap B\cap C)$$?

A
$$0.400$$

B
$$0.240$$

C
$$0.024$$

D
$$0.500$$

Solution

Given: $$A, B, C$$ are mutually independent event so this means
$$P(A\cap B\cap C)=P(A)P(B)P(C)=0.3\times 0.2\times 0.4=0.024$$
Question 6
1 / -0

Addition Theorem of Probability states that for any two events $$A$$ and $$B$$

A
$$P(A\cup B) = P(A) + P(B)$$

B
$$P(A\cup B) = P(A) + P(B) + P(A\cap B)$$

C
$$P(A\cup B) = P(A) + P(B) - P(A\cap B)$$

D
$$P(A\cup B) = P(A) \times P(B)$$

Solution

If $$A$$ and $$B$$ are any two events then the probability of happening of at least one of the events is defined as $$P(A\cup B) = P(A) + P(B)- P(A\cap B).$$
Question 7
1 / -0

The probability of complement event of impossible events is _______

A
$$0.5$$

B
$$0$$

C
$$1$$

D
$$0.46$$

Solution

The complement event of an impossible event is a possible event.
$$\therefore$$ The probability of possible events is $$1$$.
Hence, the answer is $$1$$.
Question 8
1 / -0

For any two events $$A$$ and $$B$$.

A
$$P(A) + P(B) > P(A\cap B)$$

B
$$P(A) + P(B) < P(A\cap B)$$

C
$$P(A) + P(B) \geq P(A\cap B)$$

D
$$P(A) + P(B) \leq P(A\cap B)$$

Solution

If $$A$$ and $$B$$ are any two events then the probability of happening of at least one of the events is defined as $$P(A\cup B) = P(A) + P(B)- P(A\cap B).$$
$$\implies P(A)+P(B)=P(A\cup B)+P(A\cap B)\\\implies P(A)+P(B)\ge P(A\cap B)$$
Question 9
1 / -0

If $$P(\overline {D})=\dfrac{6}{17}$$, then $$P(D)=$$

A
$$\dfrac{6}{17}$$

B
$$\dfrac{9}{17}$$

C
$$\dfrac{11}{17}$$

D
$$\dfrac{10}{17}$$

Solution

We know that,

$$P(D)+P( \overline{D})=1$$

$$\implies P(D)=1-P( \overline{D})$$

$$\implies P(D)=1-\dfrac{6}{17}$$

$$\implies P(D)=\dfrac{11}{17}$$
Question 10
1 / -0

If the letters of the word $$"ATTEMPT"$$ are written down at random. The probability that all the $$T's$$ come together is

A
$$1/21$$

B
$$6/7$$

C
$$1/7$$

D
$$1/42$$

Solution

Number of ways of arranging the words keeping all $$T's$$ together is $$5!$$
Number of ways of arranging the words is $$\dfrac{7!}{3!}$$
Probability that all the $$T's$$ together is $$\dfrac{5! }{\dfrac{7!}{3!}}=\dfrac{1}{7}$$

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Re-Attempt Weekly Quiz Competition

Probability Test - 20

Result

Probability Test - 20

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SHARING IS CARING

Question 1

Mutually exclusive events

Equally likely events

Exhaustive events

Dependent events

Solution

Question 2

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

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

$$\dfrac{2}{15}$$

$$\dfrac{6}{15}$$

Solution

Question 3

Mutually exclusive

Exhaustive

Equally likely

Independent

Solution

Question 4

$$(a^6,2a^2)$$

$$(a^2,-2a^2)$$

$$(a^3,2a^2)$$

$$(a^2,2a^3)$$

Solution

Question 5

$$0.400$$

$$0.240$$

$$0.024$$

$$0.500$$

Solution

Question 6

$$P(A\cup B) = P(A) + P(B)$$

$$P(A\cup B) = P(A) + P(B) + P(A\cap B)$$

$$P(A\cup B) = P(A) + P(B) - P(A\cap B)$$

$$P(A\cup B) = P(A) \times P(B)$$

Solution

Question 7

$$0.5$$

$$0$$

$$1$$

$$0.46$$

Solution

Question 8

$$P(A) + P(B) > P(A\cap B)$$

$$P(A) + P(B) < P(A\cap B)$$

$$P(A) + P(B) \geq P(A\cap B)$$

$$P(A) + P(B) \leq P(A\cap B)$$

Solution

Question 9

$$\dfrac{6}{17}$$

$$\dfrac{9}{17}$$

$$\dfrac{11}{17}$$

$$\dfrac{10}{17}$$

Solution

Question 10

$$1/21$$

$$6/7$$

$$1/7$$

$$1/42$$

Solution

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