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)
A die is thrown. Describe the following events:
(i) \(A: a\) number less than \(7\)
(ii) \(B: a\) number greater than \(7\)
(iii) \(C: a\) multiple of \(3\)
(iv) \(D: a\) number less than \(4\)
(v) \(E: a\) even number greater than \(4\)
(vi) \(F: a\) number not less than \(\)\(3\)
Also, find \(A∪B, A∩B, B∪C, E∩F, D∩E, A-C, D-E, E∩F', F'\)
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: \(A:\) the sum is greater than \(8\), \(B:\)\(2\) occurs on either die \(C:\)The sum is at least \(7\), and a multiple of \(3\). Which pairs of these events are mutually exclusive?