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Wile E. Coyote is pursuing the Road Runner across Great Britain toward Scotland. The Road Runner chooses his route randomly, such that there is a probability of 0.8 that he'll take the high road and 0.2 that he'll take the low road. If he takes the high road, the probability that Wile E. Catches him is 0.01. If he takes the low road, the probability he gets caught is 0.05.

Sagot :

ajeigbeibraheem

Answer:

0.444

Step-by-step explanation:

The objective is to draw the tree diagram and find the probability that the roadrunner took the high road, given that he was caught.

The tree diagram is attached in the image below:

The required probability can be computed as:

[tex]P(high\ road \ | \ caught) = \dfrac{P(high \ road \ and \ caught)} {P(caught)} \\ \\ P(high \ road \ | \ caught) = \dfrac{P(high \ road \ and \ caught)}{P(high \ road \ and \ caught)+P(low \ road \ and \ caught)}[/tex]

[tex]P(high \ road \ | \ caught) =\dfrac{ 0.8*0.01 }{ 0.80*0.01 + 0.20*0.05} \\ \\ P(high \ road \ | \ caught) = \dfrac{0.008 }{ 0.008 + 0.01} \\ \\[/tex]

[tex]P(high \ road \ | \ caught) = \dfrac{0.008 }{ 0.018}[/tex]

[tex]\mathbf{P(high \ road \ | \ caught) = 0.444}[/tex]

View image ajeigbeibraheem

The probability that he took the high road, given that he was caught is 0.444 and this can be determined by using the properties of probability.

Given :

  • The Road Runner chooses his route randomly, such that there is a probability of 0.8 that he'll take the high road and 0.2 that he'll take the low road.
  • If he takes the high road, the probability that Wile E. Catches him is 0.01.
  • If he takes the low road, the probability he gets caught is 0.05.

The required probability is given by:

[tex]\rm P = \dfrac{P(High\;road\;and\;caught)}{P(Caught)}[/tex]

[tex]\rm P = \dfrac{P(High\;road\;and\;caught)}{P(High \;road \;and \;caught)+P(Low\; road\; and \;caught)}[/tex]

[tex]\rm P=\dfrac{0.8\times 0.01}{0.8\times 0.01 + 0.2\times 0.05}[/tex]

[tex]\rm P=\dfrac{0.008}{0.018}[/tex]

P = 0.444

The probability that he took the high road, given that he was caught is 0.444.

For more information, refer to the link given below:

https://brainly.com/question/23044118

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