# Thread: Help with Some basic probability

1. ## Help with Some basic probability

Could I get some Help with basic probability

1. In a basketball tournament, suppose that the probability that the ‘better’ team wins is 0.6. Given that there are 32 teams and that only the winning team goes through after each game, what is the probability that the best team wins the tournament?

6. Show that P (A ∩ B) − P (A)P (B) = P ((A ∪ B)^c) − P (A^c)P(B^c)

7. Show that if A is independent of itself then either P (A) = 1 or P (A) = 0

Thanks

2. Originally Posted by Turloughmack
7. Show that if A is independent of itself then either P (A) = 1 or P (A) = 0
$\mathcal{P}(A)= \mathcal{P}(A\cup A)=2\cdot\mathcal{P}(A)- \mathcal{P}^2(A)$. WHY?

Can you finish this one?

3. ## basic probability

Originally Posted by Plato
$\mathcal{P}(A)= \mathcal{P}(A\cup A)=2\cdot\mathcal{P}(A)- \mathcal{P}^2(A)$. WHY?

Can you finish this one?

I dont know anymore help???

4. Originally Posted by Turloughmack
I dont know anymore help???
Can you solve $x=2x-x^2~?$

5. Yeah x=2x -x^2

so x(2-x) which means x=0 or x=2

6. So $\mathcal{P}(A)=0$.

7. Hello, Turloughmack!

1. In a basketball tournament, suppose that the probability that
the ‘better’ team wins is 0.6. .Given that there are 32 teams
and that only the winning team goes through after each game,
what is the probability that the best team wins the tournament?

I will assume a "standard" elimination.

In the first round, 16 pairs of teams play each other.
The 16 winning teams advance to the second round.

In the second round, 8 pairs of teams play each other.
The 8 winning teams advance to the third round.

In the third round, 4 pairs of teams play each other.
The 4 winning teams advance to the semi-final round.

In the semi-final round, 2 pairs of teams play each other.
The 2 winning teams advance to the final round.

In the final round, the remaing pair of teams play each other.
And the winning team wins the tournament.

There are 5 games; the best team must win all 5 games.

Therefore: . $P(\text{Best team wins}) \:=\:(0.6)^5$