Question

17 points to whoever gets these right please help <3

Answer 1

1.

Since there are 23 students in total, and 8 of them play neither sport, then the remaining 15 must play either sport. Therefore, there are
`11+13-15=9` students who play both sports.

`A` — choosing a student who plays both sports

`|\Omega|=23\\|A|=9\\\\P(A)=(9)/(23)`

2.

`A` — drawing three marbles that are blue

`6+5+4=15` — the number of all marbles

`\displaystyle\\|\Omega|=\binom{15}{3}=(15!)/(3!12!)=(13\cdot14\cdot15)/(2\cdot3)=455\\|A|=\binom{5}{3}=(5!)/(3!2!)=(4\cdot5)/(2)=10\\\\P(A)=(10)/(455)=(2)/(91)`