1. probability problem

There are 16 competitors in a table-tennis competition, 5 of which come from Racknor
Comprehensive School. Prizes are awarded to the competitors finishing in each of first,
second and third place.

Assuming that all the competitors have an equal chance of success, find the probability that
the students from Racknor Comprehensive
(a) win no prizes,
(b) win the 1st and 3rd place prizes but not the 2nd place prize,
(c) win exactly one of the prizes.

2. Can someone show what the tree diagram should look like ?

thanks.

3. Originally Posted by Tweety
There are 16 competitors in a table-tennis competition, 5 of which come from Racknor
Comprehensive School. Prizes are awarded to the competitors finishing in each of first,
second and third place.

Assuming that all the competitors have an equal chance of success, find the probability that
the students from Racknor Comprehensive
(a) win no prizes,
(b) win the 1st and 3rd place prizes but not the 2nd place prize,
(c) win exactly one of the prizes.
a) Probability that Racknor's student get 1st position: $(\frac{1}{2})^{15}$ (Because there will be 15 students to compete with)
Probability that Racknor's student get 2nd position: $(\frac{1}{2})^{14}$
Probability that Racknor's student get 3rd position: $(\frac{1}{2})^{13}$
Probability that Racknor's student get 1st,2nd,3rd position= $5P3\times$ $(\frac{1}{2})^{15}$ $\times(\frac{1}{2})^{14}$ $\times(\frac{1}{2})^{13}$

probability that the students from Racknor Comprehensive win no prizes =
1-Probability that Racknor's student get 1st,2nd,3rd position

4. Originally Posted by u2_wa
a) Probability that Racknor's student get 1st position: $(\frac{1}{2})^{15}$ (Because there will be 15 students to compete with)
Probability that Racknor's student get 2nd position: $(\frac{1}{2})^{14}$
Probability that Racknor's student get 3rd position: $(\frac{1}{2})^{13}$
Probability that Racknor's student get 1st,2nd,3rd position= $5P3\times$ $(\frac{1}{2})^{15}$ $\times(\frac{1}{2})^{14}$ $\times(\frac{1}{2})^{13}$
(a) wins no prizes: $\frac{11\cdot 10\cdot 9}{16\cdot 15\cdot 14 }$.
(b) wins the 1st and 3rd place prizes but not the 2nd place prize: $\frac{5\cdot 11\cdot 4 }{16\cdot 15\cdot 14 }$.
(c) wins exactly one of the prizes: $\frac{3\cdot 5\cdot 11\cdot 10 }{16\cdot 15\cdot 14 }$.