Sure Event

Q.

A box contains $10$ good articles and $6$ with defects. One article is chosen at random. What is the probability that its is either good or has a defect.

1. $\frac{24}{64}$

2. $\frac{40}{64}$

3. $\frac{49}{64}$

4. $\frac{64}{64}$

Q.

Bayes theorem is applicable when the events are:

1. exhaustive

2. pairwise disjoint, exhaustive and have nonzero probabilities

3. have nonzero probabilities

4. pairwise disjoint

Q.

A box contains 10 good articles and 6 defective articles. One item is drawn at random. The probability that it is either good or has a defect, is

1. $\frac{64}{64}$

2. $\frac{49}{64}$

3. $\frac{40}{64}$

4. $\frac{24}{64}$

Q. Suppose a machine produces metal parts that contain some defective parts with probability $0.05$. How many parts should be produced in order that the probability of at least one part being defective is $\frac{1}{2}$ or more?
(Given ${\log }_{10}95=1.977$ and ${\log }_{10}2=0.3)$

1. $11$
2. $12$
3. $15$
4. $14$

Q. Mark the correct alternative in the following question:

If two events are independent, then

(a) they must be mutually exclusive
(b) the sum of their probabilities must be equal to 1
(c) (a) and (b) both are correct
(d) none of the above is correct

Q.

If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then

(A) P (B|A) = 1 (B) P (A|B) = 1

(C) P (B|A) = 0 (D) P (A|B) = 0

Q.

Given that sample space S = {1, 2, 3, 4, 6} which of the following is the sure event?

1. {1, 2, 3, 4, 5}

2. {1, 2, 3, 4, 5, 6}

3. {1, 2, 3, 5, 6}

4. {1, 2, 3, 4, 6}

Q.

An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known:

P(A fails) = 0.2

P(B fails alone) = 0.15

P(A and B fail) = 0.15

Evaluate the following probabilities

(i) P(A fails| B has failed) (ii) P(A fails alone)

Q.

The sample space associated with an experiment is called the sure event?

1. True

2. False

Q.

An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known:

P(A fails) = 0.2

P(B fails alone) = 0.15

P(A and B fail) = 0.15

Evaluate the following probabilities

(i) P(A fails| B has failed) (ii) P(A fails alone)

Q. There is a box containing $30$ bulbs of which $5$ are defective. If two bulbs are chosen at random from the box in succession without replacing the first, what is the probability that both the bulbs chosen are defective?