probability tree

• How many blue pens are there in total?

  3 blue pens
• How many red pens are there in total?

  5 red pens
• What is the total number of pens Sameena has?

  8 pens
• What is the probability of selecting a red pen on the first draw?


  \(\frac{5}{8}\)
• What is the probability of selecting a blue pen on the first draw?


  \(\frac{3}{8}\)
• If the first pen selected is red, what is the probability of selecting another red pen on the second draw?


  \(\frac{4}{7}\)
• If the first pen selected is blue, what is the probability of selecting a red pen on the second draw?


  \(\frac{5}{7}\)
• If the first pen selected is blue, what is the probability of selecting another blue pen on the second draw?


  \(\frac{2}{7}\)
• What is the probability of selecting two red pens?


  \(\frac{5}{14}\)
• What is the result of multiplying \(\frac{5}{8}\) and \(\frac{4}{7}\)?


  \(\frac{20}{56}\)
• How do you simplify the fraction \(\frac{20}{56}\)?

  Divide both the numerator and denominator by their GCD, which is 4, resulting in \(\frac{5}{14}\).
• What is the final probability of selecting two red pens expressed as a decimal?

  Approximately 0.3571
• What is the final probability of selecting two red pens expressed as a percentage?

  Approximately 35.71%
• If Sameena repeats the pen selection process 100 times, how many times would you expect her to select two red pens?

  Approximately 36 times
• If an event has a probability of 0.22, how many times would you expect it to occur in 200 trials?

  Approximately 44 times
• If an event has a 30% chance of occurring, how many times would you expect it to happen in 50 trials?

  Approximately 15 times
• What are the steps to calculate the probability of selecting two red pens?

  1. Find the probability of selecting a red pen first: \(\frac{5}{8}\) 2. Find the probability of selecting a red pen second, given the first was red: \(\frac{4}{7}\) 3. Multiply these probabilities: \(\frac{5}{8} \times \frac{4}{7} = \frac{20}{56} = \frac{5}{14}\)
• How can the final probability of selecting two red pens be expressed?


  - As a fraction: \(\frac{5}{14}\) - As a decimal: approximately 0.3571 - As a percentage: approximately 35.71%
• What does a tree diagram represent in probability?

  - Shows all possible outcomes of an event - Displays the probabilities associated with each outcome