Question

Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a %20 percent chance of winning each game and that Cam has a %50 percent chance of winning each game. What is the probability that Ben will win the board game?

Answer 1

Your Answer:

Given:-

• Percentage of Justin to win a Game = 20%
• Percentage of Cam to win a Game = 50%

To find:-

• Probability of Ben to win that board game

Solution:-

In case of Justin

The chance of Justin to win the game is 20 percent that means

20% = 20/100 = 1/5

So, probability of Justin to win the game is 1/5

In Case of Cam

The chance of Cam to win the game is 50 percent

50% = 50/100 = 1/2

So, probability of Cam to win the game is 1/2

In Case of Ben

Probability of Winning the game is

P(E) = 1 - P( not E)

Here the not event is the win by Cam and Justin

So,

$\tt P(E) = 1 - ( \dfrac{1}{5}+ \dfrac{1}{2}) \\\\ \Rightarrow P(E) = 1 -\dfrac{7}{10} \\\\ \tt \Rightarrow P(E) = \dfrac{3}{10}$

So, probability of Ben to win the Game is 1/3

and the chance to win the game is 30%