Probability Quiz Set 015

The bag contains lemon flavored candies only, so the probability of orange flavored candy being taken out is zero.

Total outcomes = 36. Favorable are 6, which are: (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3). Probability = 6/36 = 1/6.

Three students have to be picked. Total number of ways = ¹¹C₃ = ${11 × 10 × 9}/{3 × 2 × 1} = $165. Number of ways of picking 1 boy and 2 girls = ⁶C₁ × ⁵C₂ = 60. So probability = $60/165$ = ${4/11}$.

Three coins will give 8 possibilities = 2 × 2 × 2. At most two tails means 1 or 2 tails. We will not get this only when all heads come, which is possible only once. So 8 - 1 = 7 chances are favorable. The probability = 7/8.

Total number of marbles is 12. Combinations of 2 marbles that are possible = ¹²C₂ = ${12 × 11}/2$ = 66. Chances of drawing a non-sky blue ball are ⁶C₂ = $(6 × (6 - 1))/2$ = 15. So probability = 15/66 = ${5/22}$.