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Data Analysis and Probability
Understanding Iikelihood
Sadie
Español
There are two boxes containing only red and black pens.
Box 
A has 4 black pens and 4 red pens.
Box 
B has 5 black pens and 15 red pens.
A pen is randomly chosen from each box.
List these events from least likely to most likely.
Event 1: choosing an orange pen from Box 
B.
Event 2: choosing a black pen from Box B.
Event 3: choosing a black or red pen from Box A.
Event 4: choosing a black pen from Box A.




Least likely

longrightarrow
Most likely


Event [్]
Event 
◻, Event 
◻
Event 
◻

Data Analysis and Probability\newlineUnderstanding Iikelihood\newlineSadie\newlineEspañol\newlineThere are two boxes containing only red and black pens.\newlineBox A \mathbf{A} has 44 black pens and 44 red pens.\newlineBox B \mathbf{B} has 55 black pens and 1515 red pens.\newlineA pen is randomly chosen from each box.\newlineList these events from least likely to most likely.\newlineEvent 11: choosing an orange pen from Box B B .\newlineEvent 22: choosing a black pen from Box B.\newlineEvent 33: choosing a black or red pen from Box A.\newlineEvent 44: choosing a black pen from Box A.\newline\begin{tabular}{|c|c|c|}\newline\hline Least likely & \longrightarrow & Most likely \\\newline\hline Event [్] & Event \square , Event \square & Event \square \\\newline\hline\newline\end{tabular}

Full solution

Q. Data Analysis and Probability\newlineUnderstanding Iikelihood\newlineSadie\newlineEspañol\newlineThere are two boxes containing only red and black pens.\newlineBox A \mathbf{A} has 44 black pens and 44 red pens.\newlineBox B \mathbf{B} has 55 black pens and 1515 red pens.\newlineA pen is randomly chosen from each box.\newlineList these events from least likely to most likely.\newlineEvent 11: choosing an orange pen from Box B B .\newlineEvent 22: choosing a black pen from Box B.\newlineEvent 33: choosing a black or red pen from Box A.\newlineEvent 44: choosing a black pen from Box A.\newline\begin{tabular}{|c|c|c|}\newline\hline Least likely & \longrightarrow & Most likely \\\newline\hline Event [్] & Event \square , Event \square & Event \square \\\newline\hline\newline\end{tabular}
  1. Calculate Event 11 Probability: Calculate the probability of Event 11: choosing an orange pen from Box B.\newlineSince there are no orange pens in Box B, the probability is 00.
  2. Calculate Event 22 Probability: Calculate the probability of Event 22: choosing a black pen from Box B. There are 55 black pens out of 2020 total pens in Box B. Probability =520=14= \frac{5}{20} = \frac{1}{4}.
  3. Calculate Event 33 Probability: Calculate the probability of Event 33: choosing a black or red pen from Box A.\newlineSince all pens in Box A are either black or red, the probability is 11.
  4. Calculate Event 44 Probability: Calculate the probability of Event 44: choosing a black pen from Box A.\newlineThere are 44 black pens out of 88 total pens in Box A.\newlineProbability =48=12= \frac{4}{8} = \frac{1}{2}.
  5. List Events by Probability: List the events from least likely to most likely based on the calculated probabilities.\newlineLeast likely: Event 11 (00 probability)\newlineNext: Event 22 (14\frac{1}{4} probability)\newlineNext: Event 44 (12\frac{1}{2} probability)\newlineMost likely: Event 33 (11 probability)

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