Theory question 113
Probability(a) Edem and his wife were invited to a dinner by a family of 5. They all sat in such a way that Edem sat next to his wife. Find the number of ways of seating them in a row.
(b) A bag contains 4 red and 5 black identical balls. If 5 balls are selected at random from the bag, one after the other with replacement, find the probability that: (i) a red ball was picked 3 times; (ii) a black ball was picked at most 2 times.
Show the model answer
Model answer
(a) 7 people; treat Edem and his wife as one unit: 6! × 2! = 1440.
(b) P(red) = 4/9, P(black) = 5/9, n = 5.
(i) ⁵C₃(4/9)³(5/9)² = 16 000/59 049 ≈ 0.271.
(ii) Black 0, 1 or 2 times: [(4/9)⁵ + 5(5/9)(4/9)⁴ + 10(5/9)²(4/9)³] = (1024 + 6400 + 16 000)/59 049 = 23 424/59 049 ≈ 0.397.
Explanation
Glue the couple together, then let them swap places.