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MCQ practice · SSC Higher Mathematics Board questions · Chapter 14: Probability

Sylhet Board 2023

When a coin with faces H and T is tossed three times in a row:

  1. i. the probability of the same result each time is 1/4
  2. ii. the probability of at most 2 H is 3/4
  3. iii. there are 8 sample points in all

Think it through first, then pick an option.

  1. a i and ii
  2. b ii and iii
  3. c i and iii
  4. d i, ii and iii
Answer and explanation

Correct answer: c i and iii

i is true: {HHH, TTT}, 2 outcomes, 2/8 = 1/4; ii is false: at most 2H means all but HHH, 7 outcomes, probability 7/8; iii is true: three steps give 2 × 2 × 2 = 8.

Why the other options are wrong

  • a i and ii: ii is false (at most 2H means all but HHH, 7 outcomes, probability 7/8), so ii has to be left out; the combination is i and iii.
  • b ii and iii: i is true ({HHH, TTT}, 2 outcomes, 2/8 = 1/4), so i has to be in the combination; the combination is i and iii.
  • d i, ii and iii: ii is false (at most 2H means all but HHH, 7 outcomes, probability 7/8), so ii has to be left out; the combination is i and iii.