True False[1 Marks ]

Question 11 Mark

State whether the statements are True or False.
The probability of an occurrence of event A is 0.7 and that of the occurrence of event B is .3 and the probability of occurrence of both is 0.4

Answer

False.
Solution:
$\text{A}\cap\text{B}\subseteq\text{A},\text{B}$
$\text{P}(\text{A}\cap\text{B})\leq\text{P(A)},\text{P(B)}$
But given that $\text{P(B)}=0.3$ and $\text{P}(\text{A}\cap\text{B})=0.4,$ which is not possible.

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Question 21 Mark

State whether the statements are True or False.
The sum of probabilities of two students getting distinction in their final examinations is 1.2

Answer

True.Solution:
Probability of each student getting distinction in their final examination is less than or equal to 1, sum of the probabilities of two may be 1.2

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Question 31 Mark

State whether the statements are True or False.
The probabilities that a typist will make 0, 1, 2, 3, 4, 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11

Answer

False.
Solution:
Sum of these probabilities must be equal to 1.
P(0) + P(1) + P(2) + P(3) + P(4) + P(5)
= 0.12 + 0.25 + 0.36 + 0.14 + 0.08 + 0.11 = 1.06 which is greater than 1, So, it is false statement.

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Question 41 Mark

State whether the statements are True or False.
The probability of intersection of two events A and B is always less than or equal to those favourable to the event A.

Answer

True.
Solution:
We know that $\text{A}\cap\text{B}\subset\text{A}$
$\text{P}(\text{A}\subset\text{B})\leq\text{P(A)}$

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Question 51 Mark

State whether the statements are True or False.
The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.

Answer

False.
Solution:
Let A = Student will pass examination
B = Student will getting compartment
P(A) = 0.73, P(B) = 0.13 and P(A or B) = 0.96
P(A or B) = P(A) + P(B) = 0.73 + 0.13 = 0.86
But P(A or B) = 0.96
Hence, given statement is false.

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Question 61 Mark

State whether the statements are True or False.
If A and B are two candidates seeking admission in an engineering College. The probability that A is selected is .5 and the probability that both A and B are selected is at most 0.3. Is it possible that the probability of B getting selected is 0.7?

Answer

False.
Solution:
Given that, $\text{P(A)}=0.5,\text{P}(\text{A}\cap\text{B})<0.3$
Now, $\text{P(A)}\times\text{P(B)}\leq0.3$
$\Rightarrow0.5\times\text{P(B)}\leq0.3$
$\Rightarrow\text{P(B)}\leq0.6$

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Question 71 Mark

State whether the statements are True or False.
The probability that a person visiting a zoo will see the giraffee is 0.72, the probability that he will see the bears is 0.84 and the probability that he will see both is 0.52.

Answer

False.
Solution:
P(to see giraffe or bear) = P (giraffe) + P (bear) - P(giraffe and bear)
=0.72 + 0.84 - 0.52 = 1.04
which is not possible.

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MATHS True False[1 Marks ]

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