Theory question 112
ProbabilityA box contains 5 blue balls, 3 black balls and 2 red balls of the same size. A ball is selected at random from the box and then replaced. A second ball is then selected. Find the probability of obtaining; (a) two red balls: (b) two blue balls or two black balls; (c) one black ball and one red ball in any order.
Show the model answer
Model answer
Total = 10 balls; draws are independent (with replacement)
(a) P(two red) = 2/10 × 2/10 = 1/25
(b) P(two blue) + P(two black) = (5/10)2 + (3/10)2 = 25/100 + 9/100 = 17/50
(c) P(black, red) + P(red, black) = 2 × 3/10 × 2/10 = 12/100 = 3/25
Explanation
'In any order' means add both orders.