Probability Questions for SBI PO

Core Definitions

Probability measures how likely an event is to happen. It always lies between 0 and 1. The sample space is the total set of all possible outcomes. An event is any subset of that sample space. Think of it like this: if you throw a die, the sample space is 6 faces. Getting an even number is your event — 3 faces out of 6.

• Probability of event A = Favourable outcomes / Total outcomes
• P(A) always lies between 0 and 1 inclusive
• P(sure event) = 1, P(impossible event) = 0
• P(not A) = 1 - P(A) — called complementary probability
• Sum of probabilities of all outcomes in sample space = 1

Addition and Multiplication Rules

Two rules power most probability questions. The Addition Rule handles OR situations — either event A or event B happens. The Multiplication Rule handles AND situations — both event A and event B happen. Mutually exclusive events cannot happen together (P(A and B) = 0). Independent events do not affect each other — like tossing two coins.

• For OR: P(A or B) = P(A) + P(B) - P(A and B)
• If mutually exclusive: P(A or B) = P(A) + P(B)
• For AND (independent): P(A and B) = P(A) x P(B)
• For AND (dependent): P(A and B) = P(A) x P(B|A)
• Drawing without replacement makes events dependent — very common in PYQs

Combinations-Based Probability

Most SBI PO questions use combinations (nCr) rather than listing outcomes. Instead of counting individual outcomes, you count groups. This is faster and less error-prone. Remember: nCr = n! / (r! x (n-r)!). Treat the denominator as total ways to select and numerator as favourable ways to select.

• Total ways to choose r items from n = nCr
• Denominator of probability = total nCr for the whole group
• Numerator = product of nCr values for each favourable sub-group
• Common setups: balls from bag, cards from deck, people in committee
• For a standard deck: 52 cards, 4 suits of 13 each, 12 face cards total

At Least / At Most Problems

At least one means one or more. Instead of adding many cases, use the complement trick: P(at least one) = 1 - P(none). This is the fastest route in exams. At most problems may need direct addition of cases but often one or two cases suffice. Always check if complement is shorter.

• P(at least one) = 1 - P(none at all) — use complement always
• P(at most one) = P(zero) + P(exactly one) — direct addition
• At least two = 1 - P(zero) - P(exactly one)
• These are the most common patterns in SBI PO Mains

• Forgetting to subtract the intersection in the Addition Rule — P(A or B) is NOT always P(A) + P(B) unless events are mutually exclusive.
• Treating without-replacement draws as independent — after each draw the total reduces, so you must update the denominator.
• Using permutations (nPr) instead of combinations (nCr) when order does not matter — leads to wrong denominator and a completely wrong answer.
• In at least problems, computing all cases one by one instead of using complement — wastes 2-3 minutes and risks arithmetic errors.
• For card problems, counting face cards as 16 (confusing picture cards) instead of 12 — there are 3 face cards per suit times 4 suits = 12 total.

• OR means ADD, AND means MULTIPLY — lock this in. When you see or in the question, add. When you see and, multiply.
• At least one: FLIP IT — P(at least 1) = 1 minus P(none). Think of flipping a coin to the other side.
• WITHOUT replacement = SHRINKING bag — both top and bottom of the fraction shrink after each draw. Remember the bag gets smaller.
• DECK cheat sheet: 52 total, 4 suits, 13 per suit, 4 aces, 12 face cards (J Q K x 4), 26 red 26 black — memorise this once, use forever.

• In SBI PO Prelims, expect 1-2 straightforward ball-from-bag or coin-toss questions. Solve using combinations directly — target under 90 seconds each.
• In SBI PO Mains, probability may appear inside a DI set where you need to find probability based on given table data — read carefully before applying formula.
• Card-based probability is a favourite in SBI PO over IBPS PO — spend 5 minutes memorising the deck composition before exam day.
• If a question looks complex with multiple draws, write out P(event) = nCr / nCr format first, then compute — avoids confusion and is faster than tree diagrams.
• Time allocation: Prelims probability questions should take 60-90 seconds. If it crosses 2 minutes, mark and move — do not let one question derail your attempt count.