Black Jack

Probability Level 3

To be accepted to the Brilliant Black Jack Team, you have to compete with Alice and Bob in three games and must win against both Alice and Bob in two successive games.

It is known that Alice is weaker than Bob, which of the playing sequence gives a higher chance to be admitted into the team?

A − B − A A-B-A B − A − B B-A-B Both yields equal chance.

View wiki
Christopher Boo by Christopher Boo , 24, Singapore

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Let's say the probability of winning against Bob is x and against Alice is y(and y>x because Alice is weaker) Then for BAB there are 2 options:

  1. You win the first and 2nd game
  2. Or you lose the first and win the other 2.

So for answer 1 the probability is: xy + (1-x)yx = xy (1+1-x) = xy(2-x)

For ABA you get:

yx + (1-y)xy = xy(1+1-y) = xy(2-y).

Since y>x the probability of BAB is larger then that of ABA. This the answer is BAB.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Anthony Holm
Oct 7, 2016

Because you must win two successive games, you must win the 2nd game. Playing this one against Alice, the weaker player, gives you an advantage in that respect.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...