Given:
Number of red marbles = 10
Number of blue marbles = 20
Number of green marbles = 30
Total marbles = 10 + 20 + 30 = 60
Number of marbles drawn = 5
Total number of possible ways to draw 5 marbles
Total outcomes =
60C5
(i) Probability that all 5 marbles are blue
Number of ways to choose 5 blue marbles from 20 =
20C5
Probability =
20C5 / 60C5
(ii) Probability that at least one marble is green
“At least one green” = 1 − (no green)
Number of non-green marbles = red + blue = 10 + 20 = 30
Number of ways to choose 5 marbles with no green =
30C5
Probability of no green =
30C5 / 60C5
Therefore,
Probability of at least one green =
1 − 30C5 / 60C5
Final Answers:
(i) Probability that all marbles are blue = 20C5 / 60C5
(ii) Probability that at least one marble is green = 1 − 30C5 / 60C5
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤5.
State true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii)A and B are mutually exclusive and exhaustive
(iii) A=B′
(iv)A and C are mutually exclusive
(v)A and B′ are mutually exclusive.
(vi) A′,B′,C are mutually exclusive and exhaustive.
From the employees of a company, \(5\) persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows: A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over \(35\) years?