Questions: Information on the weights and years of experience for a football team was obtained. The given contingency table provides a cross-classification of those data. Compute the following conditional probabilities directly; that is, do not use the conditional probability rule. A player on the football team is selected at random. Complete parts (a) through (e) below. a. Find the probability that the player selected is a rookie. P (rookie) = 0.175 (Round to three decimal places as needed.) b. Find the probability that the player selected weighs under 200 pounds. P( weighs under 200) = (Round to three decimal places as needed.) Data table Weight (lb) Years of experience ------------- Rookie 1-5 6-10 Over 10 Total Under 200 4 3 1 0 8 200-300 7 11 16 5 39 Over 300 0 11 5 0 16 Total 11 25 22 5 63

Information on the weights and years of experience for a football team was obtained. The given contingency table provides a cross-classification of those data. Compute the following conditional probabilities directly; that is, do not use the conditional probability rule. A player on the football team is selected at random. Complete parts (a) through (e) below. a. Find the probability that the player selected is a rookie. P (rookie) = 0.175 (Round to three decimal places as needed.) b. Find the probability that the player selected weighs under 200 pounds. P( weighs under 200) = (Round to three decimal places as needed.) Data table Weight (lb) Years of experience ------------- Rookie 1-5 6-10 Over 10 Total Under 200 4 3 1 0 8 200-300 7 11 16 5 39 Over 300 0 11 5 0 16 Total 11 25 22 5 63
Transcript text: Information on the weights and years of experience for a football team was obtained. The given contingency table provides a cross-classification of those data. Compute the following conditional probabilities directly; that is, do not use the conditional probability rule. A player on the football team is selected at random. Complete parts (a) through (e) below. a. Find the probability that the player selected is a rookie. P (rookie) $=0.175$ (Round to three decimal places as needed.) b. Find the probability that the player selected weighs under 200 pounds. $\mathrm{P}($ weighs under 200$)=\square$ $\square$ (Round to three decimal places as needed.) Data table \begin{tabular}{|c|c|c|c|c|c|c|} \hline \multirow{6}{*}{ Weight (lb) } & & \multicolumn{5}{|l|}{ Years of experience } \\ \hline & & \begin{tabular}{l} Rookie \\ $Y_{1}$ \end{tabular} & \begin{tabular}{l} \begin{tabular}{l} $1-5$ \\ $Y_{2}$ \end{tabular} \end{tabular} & \begin{tabular}{l} \begin{tabular}{l} $6-10$ \\ $Y_{3}$ \end{tabular} \end{tabular} & \begin{tabular}{l} Over 10 \\ $Y_{4}$ \end{tabular} & Total \\ \hline & \begin{tabular}{l} \begin{tabular}{c} Under 200 \\ $\mathrm{w}_{1}$ \end{tabular} \end{tabular} & 4 & 3 & 1 & 0 & 8 \\ \hline & \begin{tabular}{l} \begin{tabular}{c} $200-300$ \\ $w_{2}$ \\ \hline \end{tabular} \end{tabular} & 7 & 11 & 16 & 5 & 39 \\ \hline & \begin{tabular}{l} \begin{tabular}{c} Over 300 \\ $W_{3}$ \end{tabular} \end{tabular} & 0 & 11 & 5 & 0 & 16 \\ \hline & Total & 11 & 25 & 22 & 5 & 63 \\ \hline \end{tabular}
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Solution

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Solution Steps

To solve the given problems, we will use the data from the contingency table to calculate the required probabilities.

a. To find the probability that the player selected is a rookie, we will divide the total number of rookies by the total number of players.

b. To find the probability that the player selected weighs under 200 pounds, we will divide the total number of players weighing under 200 pounds by the total number of players.

Step 1: Calculate the Probability of Selecting a Rookie

To find the probability that a randomly selected player is a rookie, we use the formula for probability:

\[ P(\text{rookie}) = \frac{\text{Number of rookies}}{\text{Total number of players}} \]

Given:

  • Number of rookies = 11
  • Total number of players = 63

Substituting the values, we get:

\[ P(\text{rookie}) = \frac{11}{63} \approx 0.1746 \]

Step 2: Calculate the Probability of Selecting a Player Weighing Under 200 Pounds

To find the probability that a randomly selected player weighs under 200 pounds, we use the same probability formula:

\[ P(\text{weighs under 200}) = \frac{\text{Number of players weighing under 200}}{\text{Total number of players}} \]

Given:

  • Number of players weighing under 200 pounds = 8
  • Total number of players = 63

Substituting the values, we get:

\[ P(\text{weighs under 200}) = \frac{8}{63} \approx 0.1270 \]

Final Answer

  • The probability that the player selected is a rookie is \(\boxed{0.175}\).
  • The probability that the player selected weighs under 200 pounds is \(\boxed{0.127}\).
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