State whether the statement are True or False.The probability that a

1.	State whether the statement 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» Let A = Event that student will pass examination and B = Event that student will get compartment Then, we have P(A) = 0.73, P(B) = 0.13 and P(A ⋃ B) =0.96 Now, we have to find P(A ⋂ B) By General Addition Rule, we have P(A ⋃ B) = P(A) + P (B) – P(A ⋂ B) ⇒ P(A ⋃ B) = 0.73 + 0.13 – 0 [∵ A and B are independent events] ⇒ P(A ⋃ B) = 0.86 But P(A ⋃ B) = 0.96 Hence, the given statement is False.

State whether the statement 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»

Let A = Event that student will pass examination

and B = Event that student will get compartment

Then, we have

P(A) = 0.73, P(B) = 0.13 and P(A ⋃ B) =0.96

Now, we have to find P(A ⋂ B)

By General Addition Rule, we have

P(A ⋃ B) = P(A) + P (B) – P(A ⋂ B)

⇒ P(A ⋃ B) = 0.73 + 0.13 – 0

[∵ A and B are independent events]

⇒ P(A ⋃ B) = 0.86

But P(A ⋃ B) = 0.96

Hence, the given statement is False.

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State whether the statement 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.

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