Theory question 104
Probability(a) Two fair dice are thrown once. Find the probability of getting: (i) the same digit (ii) a total score greater than 5.
(b) Given that x = cos 30° and y = sin 30°, evaluate without using a mathematical table or calculator: (x2 + y2)/(y2 − x2).
Show the model answer
Model answer
(a)(i) Doubles (1,1)…(6,6): 6/36 = 1/6.
(ii) Totals of 5 or less: 1 + 2 + 3 + 4 = 10 outcomes, so P(total > 5) = 1 − 10/36 = 26/36 = 13/18.
(b) x2 + y2 = 3/4 + 1/4 = 1; y2 − x2 = 1/4 − 3/4 = −1/2. Value = 1 ÷ (−1/2) = −2.
Explanation
Count the outcomes that are not wanted when that is easier, then subtract from 1.