Respuesta :
From the four possible guesses listed below, for the Terrence the highest chance of success is selecting black or pink square tile and blue or green round tile.
What do you mean by chain rule in probability?
For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
Here P(A|B) is probability of occurrence of A given that B already occurred.
Terrence is playing a game in which he will randomly select one square tile and one round tile from the tile sets shown below.
Before he does so, he tries to guess which tiles he will draw.
- Square tiles: 12 blue, 20 yellow, 8 red, 6 green, 4 pink, 5 black, 3 brown, 2 white, total 60.
- Round tiles: 9 black, 4 green, 3 yellow, 2 white, 6 blue, 12 red, total 36.
Here, the event of choosing round tile and square tile is independent to each other.
- a. black or pink square tile and blue or green round tile
The chance of black or pink square tile and blue or green round tile is,
[tex]P_1=\dfrac{5+4}{60}\times\dfrac{12+6}{36}\\P_1=\dfrac{9}{60}\times\dfrac{18}{36}\\P_1=0.65[/tex]
- b. yellow square tile and yellow round tile
The chance of yellow square tile and yellow round tile is,
[tex]P_2=\dfrac{20}{60}\times\dfrac{3}{36}\\P_2=0.42[/tex]
- c. green, brown, or white square tile and black or white round tile
The chance of green, brown, or white square tile and black or white round tile is,
[tex]P_3=\dfrac{6+3+2}{60}\times\dfrac{9+2}{36}\\P_3=\dfrac{11}{60}\times\dfrac{11}{36}\\P_3=0.49[/tex]
- d. red square tile and red or white round tile
The chance of red square tile and red or white round tile is,
[tex]P_4=\dfrac{8}{60}\times\dfrac{12+2}{36}\\P_4=\dfrac{8}{60}\times\dfrac{14}{36}\\P_4=0.52[/tex]
Thus, from the four possible guesses listed below, for the Terrence the highest chance of success is selecting black or pink square tile and blue or green round tile.
Learn more about chain rule here:
https://brainly.com/question/21081988
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