Question:
You play tennis against a player that you have a 20% chance of winning. What is the probability that you win no game out of 6 games?
Answer:
[tex]Probability = 0.262144[/tex]
Step-by-step explanation:
Represent the probability of winning with P(Win)
[tex]P(Win) = 20\%[/tex]
Required
Determine the probability of not winning 6 games
First, we calculate the probability of not winning a game.
Opposite probability add up to 1.
So, we have:
[tex]P(Win) + P(Lose) = 1[/tex]
[tex]P(Lose) = 1 - P(Win)[/tex]
[tex]P(Lose) = 1 - 20\%[/tex]
[tex]P(Lose) = 100\% - 20\%[/tex]
[tex]P(Lose) = 80\%[/tex]
The sample space of losing 6 games is:
Lose Lose Lose Lose Lose Lose
Therefore, the probability is:
[tex]Probability = 80\% *80\% *80\% *80\% *80\% *80\%[/tex]
[tex]Probability = 0.80*0.80*0.80*0.80*0.80*0.80[/tex]
[tex]Probability = 0.262144[/tex]
