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  1. LPU MCA Semester 1
  2. PEA515
  3. Unit 5

PEA515 · Unit 5: Permutation, combination and probability

Conditional probability

30 practice questions · in the ETE syllabus

Practise this topicPractise this topic

Key points

  • P(A given B) = P(A and B) / P(B)
  • The condition reduces the sample space
  • Without replacement, the second draw has fewer cards
  • Independent events multiply

Conditional probability P(A | B) is the probability of A given that B has happened. The condition shrinks the sample space to B, so

P(A | B) = P(A and B) / P(B).

SituationResult
First die shows 4, sum at least 6Only 6 outcomes remain; the second die must be 2 or more, so 5/6
Two cards without replacement, first is a king51 cards remain and 3 are kings, so 3/51 = 1/17
Group data: 62 drink tea, 48 drink bothP(coffee given tea) = 48/62 = 24/31
Independent eventsP(A and B) = P(A) x P(B), and P(A given B) = P(A)
Bayes-type questionCompare the defective items of one source with all defective items

For independent events A and B with P(A) = 1/3 and P(B) = 1/2: P(A or B) = 1/3 + 1/2 - 1/6 = 2/3, and P(neither) = (2/3)(1/2) = 1/3.

In a Bayes-type problem, if machine A makes 40% of items with 2% defective and B makes 60% with 3% defective, then P(A given defective) = (40 x 2) / (40 x 2 + 60 x 3) = 80 / 260 = 4/13.

Exam trap: divide by the size of the condition, not by the whole sample space.

Try two questions

Question 1 · Tier 3, Apply

Two fair dice are thrown. Given that the first die shows 2, what is the probability that the sum is at least 7?

  1. 1/18
  2. 7/12
  3. 1/3
  4. 1/6
Show the answer

C. With the first die fixed at 2, the second die must be at least 5: 2 of 6 outcomes.

Why not A: Divides by all 36 outcomes instead of the 6 that remain.

Why not B: Ignores the information about the first die.

Why not D: Treats the outcome as a single face.

Question 2 · Tier 4, Analyse

In a group of 60 people, 25 drink tea, 35 drink coffee and 8 drink both. If a person who drinks tea is chosen at random, what is the probability that the person also drinks coffee?

  1. 8/35
  2. 8/25
  3. 2/15
  4. 7/12
Show the answer

B. Of the 25 tea drinkers, 8 also drink coffee: 8/25.

Why not A: Divides by the wrong group.

Why not C: Gives the probability of both without the condition.

Why not D: Gives the unconditional probability.