Question 1 of 55intermediate🔧 ApplyNumerical4 marks
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that (i) all will be blue? (ii) atleast one will be green?
(i)
Answer
P(all blue) = C(20,5)/C(60,5) = 15504/5461512 = 646/227563
(ii)
Answer
P(at least one green) = 1 - C(30,5)/C(60,5) = 1 - 142506/5461512 = 4367/4484
Explanation
This question from Miscellaneous Exercise on Chapter 14 tests understanding of combinations in probability. For part (i), we calculate probability of selecting all blue marbles. For part (ii), we use the complement rule: P(at least one green) = 1 - P(no green), which is more efficient than calculating multiple cases.