Theory question 109
Probability(a) If a number is chosen at random from the integers 5 to 25 inclusive, find the probability that the number is a multiple of 5 or 3.
(b) A bag contains 10 balls that differ only in colour; 4 are blue and the others are red. Two balls are picked, one after the other with replacement. What is the probability that (i) both are red? (ii) both are the same colour?
Show the model answer
Model answer
(a) 21 integers. Multiples of 5: 5, 10, 15, 20, 25. Multiples of 3: 6, 9, 12, 15, 18, 21, 24. 15 is in both, so 11 numbers. P = 11/21
(b) P(red) = 6/10, P(blue) = 4/10
(i) 6/10 × 6/10 = 9/25
(ii) 9/25 + (4/10 × 4/10) = 9/25 + 4/25 = 13/25
Explanation
Count a number like 15 that is a multiple of both only once.