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
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?