Probability — Practice

Question 1

If a coin is tossed, what is the probability of getting a head?

Accepted Answer

✦ Answer: Sample space = {H, T}. Favourable = {H}. P(H) = 1/2.

Question 2

A card is drawn from a deck of 52. Find P(face card) and P(red face card).

Accepted Answer

Step 1 — Face cards.
  Face cards: J, Q, K of each suit (4 suits × 3 = 12 face cards)

Step 2 — P(face card).
  P = 12/52 = 3/13

Step 3 — Red face cards.
  Red suits: Hearts, Diamonds (2 suits × 3 face cards = 6)

Step 4 — P(red face card).
  P = 6/52 = 3/26

✦ Answer: P(face card) = 3/13; P(red face card) = 3/26.

Question 3

Two dice are rolled. Find P(sum = 7), P(sum > 9), and P(doubles).

Accepted Answer

Step 1 — Total outcomes.
  6 × 6 = 36

Step 2 — P(sum = 7).
  Combinations: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — 6 outcomes
  P(sum=7) = 6/36 = 1/6

Step 3 — P(sum > 9), i.e., sum 10, 11, or 12.
  Sum 10: (4,6), (5,5), (6,4) — 3 outcomes
  Sum 11: (5,6), (6,5) — 2 outcomes
  Sum 12: (6,6) — 1 outcome
  Total: 6 outcomes
  P(sum>9) = 6/36 = 1/6

Step 4 — P(doubles).
  Doubles: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) — 6 outcomes
  P(doubles) = 6/36 = 1/6

Step 5 — Verify.
  All values 6/36 = 1/6 ✓

✦ Answer: P(sum=7) = P(sum>9) = P(doubles) = 1/6.

Practice — Probability

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