IC 2.3-25: Small Spaces and Combinations Exercise 1. Eight identical tiles, numb
ID: 2931497 • Letter: I
Question
IC 2.3-25: Small Spaces and Combinations Exercise 1. Eight identical tiles, numbered 1 through 8, are placed in a bag The bag is shaken, and three are removed at random. If you treat selections as sets of three, then the size of the sample space is under 100. (A) What is the size of the sample space? B) What is the chance that the selected numbers sum to 13 (C) What is the chance that the 7 tile is not selected? (D) What is the chance that 7 is the highest value on the selected tiles? E) What is the chance that no two of the selected tiles have adjacent number? (For example, if the 1 is selected, then the 2 is not, or if the is selected, than neither the 3 nor the 5 is on another selection.)Explanation / Answer
Solution:-
2)
Number of red marbles = 7
Number of blue marbles = 4
Number of white marbles = 6
a) The chance that no red marble is selected is 0.0407.
Total number of marbles = 7 + 4 + 6 = 17
Number of non red balls = 10
Total number of ways of selecting 5 marbles = 17C5 = 6188
Number of ways of selecting non red balls = 10C5 = 252
The chance that no red marble is selected = 252/6188 = 0.0407
b) The chance that exactly two red marbles are selected is 0.4072
Number of red and white balls = 7 + 6 = 13
Total number of ways of selecting 5 marbles = 17C5 = 6188
Number of ways of selecting exactly two red balls = 7C2 × 10C3 = 2520
The chance that exactly two red marbles are selected = 2520/6188 = 0.4072
c) The chance that only red and white marbles are selected is 0.208.
Number of red balls = 7
Total number of ways of selecting 5 marbles = 17C5 = 6188
Number of ways of selecting exactly two red balls = 13C5= 1287
The chance that only red and white marbles are selected = 1287/6188 = 0.208
d) The chance that the selection consists of two red marbles, two blue marbles and one white marbles is 0.1222.
Number of red balls = 7
Total number of ways of selecting 5 marbles = 17C5 = 6188
Number of ways of selecting exactly two red balls = 7C2× 4C2× 6C1 = 756
The chance that the selection consists of two red marbles, two blue marbles and one white marbles = 756/6188 = 0.1222