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Test: Conditional Probability - Electronics and Communication Engineering (ECE) MCQ


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10 Questions MCQ Test - Test: Conditional Probability

Test: Conditional Probability for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Test: Conditional Probability questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Conditional Probability MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Conditional Probability below.
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Test: Conditional Probability - Question 1

If P(A) = 5/13, P(B) = 7/13 and P(A∩B) = 3/13, evaluate P(A|B).

Detailed Solution for Test: Conditional Probability - Question 1

We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
Which is equivalent to (3/13) / (7/13), hence the value of P(A|B) = 3/7.

Test: Conditional Probability - Question 2

If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________

Detailed Solution for Test: Conditional Probability - Question 2

We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
Also P(A∪B) = P(A)+P(B) – P(A∩B). (By formula of probability)
⇒ 8/11 = 7/11 + 6/11 – P(A∩B)
⇒ P(A∩B) = 13/11 – 8/11
⇒ P(A∩B) = 5/11
P(A|B) = (5/11) / (6/11).
P(A|B) = 5/6

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Test: Conditional Probability - Question 3

Given that E and F are events such that P(E) = 0.5, P(F) = 0.4 and P(E∩F) = 0.3, then what will be the value of P(F|E)?

Detailed Solution for Test: Conditional Probability - Question 3

We know that P(F|E) = P(E∩F) / P(E). (By formula for conditional probability)
Value of P(E∩F) is given to be 0.3 and value of P(E) is given to be 0.5.
P(F|E) = (0.3) / (0.5).
P(F|E) = 3 / 5.

Test: Conditional Probability - Question 4

If P(A) = 1/5, P(B) = 0, then what will be the value of P(A|B)?

Detailed Solution for Test: Conditional Probability - Question 4

We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
The value of P(B) = 0 in the given question. As the value of denominator becomes 0, the value of P(A|B) becomes un-defined.

Test: Conditional Probability - Question 5

Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F), then value of P(F|F) is __________

Detailed Solution for Test: Conditional Probability - Question 5

We know that P(S|F) = P(S∩F) / P(F). (By formula for conditional probability)
Which is equivalent to P(F|F) = P(F) / P(F) = 1, hence the value of P(F|F) = 1.

Test: Conditional Probability - Question 6

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E∩F) = 0.2, then P(E|F) ?

Detailed Solution for Test: Conditional Probability - Question 6

We know that P(E|F) = P(E∩F) / P(F). (By formula for conditional probability)
Value of P(E∩F) is given to be 0.2 and value of P(F) is given to be 0.3.
P(E|F) = (0.2) / (0.3).
P(E|F) = 2 / 3.

Test: Conditional Probability - Question 7

If E and F are two events associated with the same sample space of a random experiment then P (E|F) is given by _________

Detailed Solution for Test: Conditional Probability - Question 7

E and F are two events associated with the same sample space of a random experiment.
The value of P (E|F) = (E∩F) / P(F), provided P(F) ≠ 0. We know that if P(F) = 0, then the value of P(E|F) will reach a value which is not defined hence it is wrong option. Also, P(E∩F) / P(F) and P(E∩F) / P(E) are wrong and do not equate to P(E|F).

Test: Conditional Probability - Question 8

You have two bags of colored marbles. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. You choose one of the bags at random and then select a marble from that bag. What is the probability that you selected Bag A, given that you picked a red marble?

Detailed Solution for Test: Conditional Probability - Question 8

Let's use conditional probability here. We want to find the probability of selecting Bag A given that a red marble was chosen.

P(A) is the probability of choosing Bag A, and P(R) is the probability of choosing a red marble.

We know that P(A) is 1/2 because we choose a bag at random, and there are two bags.

P(R|A) is the probability of choosing a red marble from Bag A, which is 3/5.

P(R|B) is the probability of choosing a red marble from Bag B, which is 4/5.

Now, we can use Bayes' theorem to find P(A|R), the probability of choosing Bag A given a red marble was picked:

P(A|R) = [P(R|A) * P(A)] / [P(R|A) * P(A) + P(R|B) * P(B)]

P(A|R) = (3/5 * 1/2) / [(3/5 * 1/2) + (4/5 * 1/2)]

P(A|R) = (3/10) / [(3/10) + (4/10)]

P(A|R) = (3/10) / (7/10)

P(A|R) = 3/7

So, the probability of selecting Bag A, given that a red marble was chosen, is 3/7, which corresponds to option D.

Test: Conditional Probability - Question 9

In a deck of 52 cards, there are 26 red cards (hearts and diamonds) and 26 black cards (spades and clubs). If you draw two cards without replacement, what is the probability that the first card is red and the second card is also red?

Detailed Solution for Test: Conditional Probability - Question 9

To find the probability that the first card is red and the second card is also red, we can use conditional probability.

First, the probability that the first card is red is 26/52 because there are 26 red cards out of 52 in the deck.

Now, after drawing a red card, there are 25 red cards left in a deck of 51 cards (one card has already been drawn).

So, the probability that the second card is also red, given that the first card was red, is 25/51.

Therefore, the probability of both events happening is the product of these two probabilities:

P(First card is red and Second card is red) = (26/52) * (25/51)

Simplifying this:

P(First card is red and Second card is red) = (1/2) * (25/51)

P(First card is red and Second card is red) = 25/102

So, the correct answer is option C, which is 25/102.

Test: Conditional Probability - Question 10

P and Q are considering to apply for a job. The probability that P applies for the job is 1/4, the probability that P applies for the job given that Q applies for the job is 1/2, and the probability that Q applies for the job given that P applies for the job is 1/3. Then the probability that P does not apply for the job given that Q does not apply for the job is

Detailed Solution for Test: Conditional Probability - Question 10

Data:

Formula

Calculation:

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