Tayarri LCAT
LCAT Math, Problem-Solving and Data Analysis

Probability for the LCAT: lesson and practice

Probability = favorable outcomes ÷ total outcomes. In a two-way table, the key is the denominator: if the question says "if a person from group X is chosen", divide by group X’s total only. For independent events, "both" means multiply; "not" means subtract from 1.

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No calculator on the LCAT. LUMS’s official guidelines say calculators are not allowed, so every practice question here can be solved by hand.
Question wordingDenominator
"chosen at random from all…"Grand total
"If a Grade 11 student is chosen…"Grade 11 row total
"If a student who chose science is chosen…"Science column total
Cover every row or column that is not part of the "if" group before you calculate.

Common mistakes

Dividing by the grand totalConditional questions limit the group.
Adding for "both"Independent events multiply.
Forgetting the complementP(not A) = 1 − P(A).

Sample questions with answers

1. 6 red, 3 blue and 2 green marbles. P(blue)?
  1. 3/8
  2. 3/11 (correct)
  3. 1/3
  4. 8/11

3 out of all 11 marbles.

2. Morning shift: 30 walked, 24 used transport. If a morning worker is chosen, P(walked)?
  1. 30/91
  2. 5/9 (correct)
  3. 15/28
  4. 54/91

30 out of the 54 morning workers.

3. P(rain) = 2/5. P(no rain)?
  1. 2/5
  2. 3/5 (correct)
  3. 2/3
  4. 1/5

1 − 2/5 = 3/5.

Frequently asked questions

What is conditional probability?

The probability of an event within a limited group, calculated using that group’s total as the denominator.

When do I multiply probabilities?

When both of two independent events must happen.

Is probability tested on the LCAT?

Yes. It falls under Problem-Solving and Data Analysis, one of the content domains LUMS lists for the LCAT in its official sample questions.

Can I practice this without a calculator?

Yes. Every practice question here can be solved by hand, because calculators are not allowed on the LCAT.

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