Probability in Video Games

Adapted from Course materials (II.A Student Activity Sheet 5) for AMDM developed under the leadership of the Charles A. Dana Center, in collaboration with the Texas Association of Supervisors of Mathematics and with funding from Greater Texas Foundation.

Lisa is playing a game on her smartphone in which the object is to find hidden keys. To do so, she must roam through several levels, opening with doors. In one part of the journey, Lisa must pass through two doors (Door 1, then Door 2) to get to the next level.

Hidden Keys

The chance that Door 1 is open is 20%

The chance that Door 2 is open is 30%

The game designer has programmed the gates so that the probability of both being open at the same time is 0.1.

Draw a model of the situation to help you answer related questions.

Which model did you use? Why? Watch the video below each diagram to see how it was created.

Venn Diagram

Tree Diagram

Answer the following questions yourself before asking the characters.

Question #1

What is the probability that both gates are open when Lisa reaches this part of the game?

The game designer has programmed the doors so that both are simultaneously open 10% of the time. This probability is shown in the intersection of both the Venn Diagram and the area Model.

Question #2

What is the probability that only door 1 is open when Lisa reaches this part of the game? What about only door 2?

The probability of door 1 being open is 20 %. Part of that is time, door 2 is also open, so p ( only door 1 open) = 10/100 or 10%

Question #3

What is the probability that neither gate is open when Lisa reaches this part of the game?

Door 1 is open 10% of the time, Door 2 is open 20% of the time, and both are concurrently open 10% of the time. This means that one or both doors are open 40 % of the time. If you are using the Venn Diagram, the probability that Door 1 and Door 2 are not open is the area outside of the circle.

Question #4

What is the probability that Lisa finds exactly one door open?

To find exactly one door open means one of the doors is open and the other is not. The following events justify the results:

Door 1 open and Door 2 closed
Door 1 closed and Door 2 open.

There are mutually exclusive events therefore, the probability is .10 +.20 =.30 or 30%

Bonus Round

Self-Assessment: The Bonus Level

Lisa played the game until she made it to the bonus levels. If she zaps a target in one try, Lisa gets a chance to capture a bonus shield. To capture the bonus shield, she must hit a second target in one try. Lisa can hit a target in one try an average of 60% of the time.

Answer the following questions.

What is the probability that Lisa hits the first target?
P ( Hit first) = 60 %, or 3 out of 5 times Lisa hits the target because she can hit a target 60 % of the time.
What is the probability that Lisa captures the bonus shield?
To capture the bonus shield, Lisa must hit the second target. Since she can hit a target 60 % of the time, find 60 % of 60 % This means the probability of hitting the second target and capturing the bonus shield is 36%
What is the probability that Lisa hits the target and does not hit the second target to capture the shield?
To hit the first target but not capture the shield Lisa has to hit the target and miss the second target. The probability of hitting the first target is 60% and the probability of missing the second target is 40%. Therefore the probability of hitting the first target and not capturing the shield is 74%.

IMAGES CREATED BY GAVS