Probability

• What is an experiment in probability?

  A repeatable process with outcomes
• What is an event in probability?

  A collection of one or more outcomes
• What is a sample space?

  The set of all possible outcomes
• How can probabilities be expressed?

  As decimals or fractions
• What is the range of probabilities?

  0 (impossible) to 1 (certain)
• How do you calculate the probability of an event?

  Number of outcomes in event / total outcomes
• What is the probability of finishing the number puzzle in under 9 minutes?

  • Total students: 50
  • Students under 9 minutes: 19
  • Probability: $\frac{19}{50}$
• How do you estimate the probability of finishing in over 10.5 minutes?

  • 10.5 minutes falls in 9 ≤ 𝑡 < 11
  • Estimate: $\frac{1}{4} \times 12 =$$3$
  • Total students over 10.5 minutes: 22
  • Probability: $\frac{22}{50}$
• What is a Venn diagram used for?

  To represent events graphically
• What does a rectangle represent in a Venn diagram?

  The sample space, S
• What does a tree diagram show?

  The outcomes of events in succession
• How do you find the probability that both beads drawn are green?

  1. Draw a tree diagram
  2. Multiply along branches:

  • $P(green and green) =$$\frac{7}{12} \times \frac{6}{11} =$$\frac{3}{11}$
• How do you calculate the probability of drawing beads of different colors?

  • $P(different colours) =$$P(green then blue) +$$P(blue then green)$
  • <latex=P(green then blue) = \frac{7}{12} \times \frac{5}{11}</latex>
  • <latex=P(blue then green) = \frac{5}{12} \times \frac{7}{11}</latex>
  • Total: <latex=\frac{35}{66}</latex>
• What are mutually exclusive events?

  Events with no outcomes in common
• How is the probability of mutually exclusive events calculated?

  P(A or B) = P(A) + P(B)
• What defines independent events?

  One event has no effect on another
• How do you check if events are independent?

  Compare P(A and B) with P(A) × P(B)
• How do you find the probability of watching shows B or C or both?

  • Total watching B or C: 26
  • Probability: <latex=\frac{26}{total students}</latex>
• How do you determine if watching A and B are independent?

  Check if P(A and B) equals P(A) × P(B)
• What does the intersection of A and B represent?

  • The event where both A and B occur
• What does the union of A and B represent?

  • The event where either A or B or both occur
• What does the shaded area in a Venn diagram show?

  • The event in which A does not occur