Given:
Total number of tickets = 10,000
Number of prizes = 10
Number of winning tickets = 10
Number of non-winning tickets = 9,990
(a) Probability of not getting a prize if one ticket is bought
Probability =
Number of non-winning tickets / Total tickets
= 9990 / 10000
= 999 / 1000
(b) Probability of not getting a prize if two tickets are bought
Probability that both tickets are non-winning =
(9990 / 10000) × (9989 / 9999)
= (9990 × 9989) / (10000 × 9999)
(c) Probability of not getting a prize if ten tickets are bought
Probability that all ten tickets are non-winning =
(9990 / 10000) × (9989 / 9999) × (9988 / 9998) × … × (9981 / 9991)
= (9990 × 9989 × 9988 × … × 9981) / (10000 × 9999 × 9998 × … × 9991)
Final Answers:
(a) Probability = 999 / 1000
(b) Probability = (9990 × 9989) / (10000 × 9999)
(c) Probability = (9990 × 9989 × 9988 × … × 9981) / (10000 × 9999 × 9998 × … × 9991)
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?