Theory question 112
ProbabilityA box contains 5 red, 7 blue and 4 green identical bulbs. Two bulbs are picked at random from the box without replacement. Calculate the probability of picking (a) same colour of bulbs; (b) different colour of bulbs; (c) at least one red bulb.
Show the model answer
Model answer
16 bulbs; 16 × 15 = 240 ordered pairs.
(a) (5×4 + 7×6 + 4×3)/240 = 74/240 = 37/120.
(b) 1 − 37/120 = 83/120.
(c) 1 − P(no red) = 1 − (11/16)(10/15) = 1 − 11/24 = 13/24.
Explanation
'Different colour' is the complement of 'same colour'.