you are playing a game in which you randomly select one square tile and one round tile from the sets shown…

you are playing a game in which you randomly select one square tile and one round tile from the sets shown below. before you select your tiles, you try to guess which combination you will pick. of the four possible guesses listed below, which one will give you the greatest chance of success? a. green square tile and red round tile b. pink square tile and orange or yellow round tile c. red or blue square tile and black or green round tile d. blue square tile and blue or purple or white round tile

you are playing a game in which you randomly select one square tile and one round tile from the sets shown below. before you select your tiles, you try to guess which combination you will pick. of the four possible guesses listed below, which one will give you the greatest chance of success? a. green square tile and red round tile b. pink square tile and orange or yellow round tile c. red or blue square tile and black or green round tile d. blue square tile and blue or purple or white round tile

Answer

Answer:

b. pink square tile and orange or yellow round tile

Explanation:

Step1: Count square tiles

There are 40 square - tiles in total. Green: 12, Pink: 12, Red: 8, Blue: 8, Yellow: 8.

Step2: Count round tiles

There are 30 round - tiles in total. Red: 4, Orange: 5, Yellow: 3, Black: 4, Green: 3, Blue: 9, Purple: 5, White: 1.

Step3: Calculate probabilities for option a

Probability of green square tile: $\frac{12}{40}=\frac{3}{10}$. Probability of red round tile: $\frac{4}{30}=\frac{2}{15}$. Combined probability: $\frac{3}{10}\times\frac{2}{15}=\frac{6}{150}=\frac{1}{25}$.

Step4: Calculate probabilities for option b

Probability of pink square tile: $\frac{12}{40}=\frac{3}{10}$. Probability of orange or yellow round tile: $\frac{5 + 3}{30}=\frac{8}{30}=\frac{4}{15}$. Combined probability: $\frac{3}{10}\times\frac{4}{15}=\frac{12}{150}=\frac{2}{25}$.

Step5: Calculate probabilities for option c

Probability of red or blue square tile: $\frac{8+8}{40}=\frac{16}{40}=\frac{2}{5}$. Probability of black or green round tile: $\frac{4 + 3}{30}=\frac{7}{30}$. Combined probability: $\frac{2}{5}\times\frac{7}{30}=\frac{14}{150}=\frac{7}{75}$.

Step6: Calculate probabilities for option d

Probability of blue square tile: $\frac{8}{40}=\frac{1}{5}$. Probability of blue or purple or white round tile: $\frac{9+5 + 1}{30}=\frac{15}{30}=\frac{1}{2}$. Combined probability: $\frac{1}{5}\times\frac{1}{2}=\frac{1}{10}=\frac{15}{150}$. Since $\frac{2}{25}=\frac{12}{150}$ is the largest among $\frac{1}{25},\frac{12}{150},\frac{7}{75},\frac{15}{150}$, option b has the greatest chance of success.