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you play tennis against a player that you have a 20% chance of winning. what is the probability g

Sagot :

MrRoyal

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]

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