SIG Expected Value 2027: Card Draw Primes Question

The answer is 7/3, or about 2.33. The primes between 1 and 18 are 2, 3, 5, 7, 11, 13, 17 (seven), so each draw is prime with probability 7/18. By linearity of expectation over 6 draws: E(X) = 6 × 7/18 = 7/3. This "sig cards prime expected value" question is commonly reported by candidates as a linearity-of-expectation check.

SIG Cards Prime Expected Value: What This Question Assesses

The question tests whether you reach for linearity of expectation instead of computing the full binomial distribution. You do not need P(X = k) for each k — you just need the per-draw probability. SIG wants this reflex because pricing complex positions almost always decomposes into sums of simple expectations.

SIG Cards Prime Expected Value: How to Answer

• Count the primes. Between 1 and 18: 2, 3, 5, 7, 11, 13, 17 — seven primes. (Note 1 is not prime.)
• Get the per-draw probability. Each draw is prime with probability 7/18. Replacement means every draw is identical and independent.
• Apply linearity of expectation. E(X) = sum of expectations = 6 × 7/18 = 42/18 = 7/3 ≈ 2.33.
• Note what you avoided. No binomial coefficients, no distribution of X — linearity works whether or not the draws are independent.

Sample line: "Seven of the eighteen cards are prime, so each draw contributes 7/18 of expected value — times six draws, that's 7/3, about 2.33."

Common Mistakes

• Counting 1 as prime, which gives 8/18 per draw and the wrong answer.
• Computing the full binomial distribution — correct but far too slow for an interview setting.
• Thinking replacement matters for the expectation — it affects the variance, not the mean; linearity of expectation needs no independence.

If you started expanding binomial terms, drill linearity-of-expectation problems until it is your first move. Question formats may vary by role and region; confirm on SIG's official careers page.

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FAQ

What is E(X) when drawing 6 times with replacement from cards 1–18? 7/3 ≈ 2.33 — six draws times the per-draw prime probability of 7/18.

Which numbers between 1 and 18 are prime? 2, 3, 5, 7, 11, 13, 17 — seven numbers. 1 is not prime.

Does linearity of expectation require independence? No — that is the point. It holds for any collection of random variables, dependent or not.

Is this a real SIG interview question? Card-draw and linearity-of-expectation questions are commonly reported by candidates in SIG interviews, though exact versions may vary by role and region.

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