Probability Rules and Tree Diagrams
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 368 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Probability Rules and Tree Diagrams — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionSet Notation and Venn Diargram NotationsConcept Practice
2 marks~3 minCriterion A
A school records whether each student in a group of 80 studies French (FF) and whether they study Spanish (SS). The results are displayed in the Venn diagram below.

Identify the region of the Venn diagram that represents F∩SF \cap S, and explain what membership of this region means for a student in the group. [2]
Question diagram

Solutions

2QuestionSolving Problems using tree diagrams and Venn DiagramsAssessment Practice
4 marks~6 minCriterion C
A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn without replacement. The tree diagram shows the following probabilities:

First draw: P(Red)=410P(\text{Red}) = \dfrac{4}{10}, P(Blue)=610P(\text{Blue}) = \dfrac{6}{10}

Second draw (after Red): P(Red∣Red)=39P(\text{Red} \mid \text{Red}) = \dfrac{3}{9}, P(Blue∣Red)=69P(\text{Blue} \mid \text{Red}) = \dfrac{6}{9}

Second draw (after Blue): P(Red∣Blue)=49P(\text{Red} \mid \text{Blue}) = \dfrac{4}{9}, P(Blue∣Blue)=59P(\text{Blue} \mid \text{Blue}) = \dfrac{5}{9}
a
State the probability of drawing a red marble second, given that the first marble drawn was red. [1]
b
Show that the two draws are dependent events by comparing the conditional probabilities of drawing a red marble second with the unconditional probability of drawing a red marble first. [2]
c
A quality-control inspector claims that, for a fair sampling process, the colour drawn first should have no influence on subsequent draws. Advise the inspector whether this bag of marbles satisfies that claim when sampling without replacement. [1]
Question diagram

Solutions

3QuestionCalculating Combined ProbabilitiesAssessment Practice
4 marks~6 minCriterion D
A meteorologist models rainfall using a Markov chain. The probability of rain on Day 1 is 0.40.4. Given rain today, the probability of rain tomorrow is 0.70.7; given no rain today, the probability of rain tomorrow is 0.20.2.
a
Construct a tree diagram showing all possible weather outcomes for three consecutive days, labelling every branch with its probability. [1]
b
Calculate the probability that it rains on exactly two of the three days. [2]
c
The meteorologist claims this model is reliable enough to issue a public rain warning whenever the probability of rain on Day 3 exceeds 0.50.5. After two consecutive rainy days, advise the meteorologist whether the model alone is sufficient justification for issuing a public warning. [1]
Question diagram

Solutions

4QuestionQualitative handling of probabilityAssessment Practice
5 marks~8 minCriterion B
The diagram shows the first four figures of a pattern made from small equilateral triangles.

Figure 11 shaded triangle0 unshaded triangles.
Figure 21 shaded triangle3 unshaded triangles.
Figure 31 shaded triangle8 unshaded triangles.
Figure 41 shaded triangle15 unshaded triangles.


The total number of small triangles in Figure nn is denoted T(n)T(n).
a
Write down the values of T(1)T(1), T(2)T(2), T(3)T(3), and T(4)T(4). [1]
b
Find a rule for T(n)T(n) in the form T(n)=an2+bT(n) = an^2 + b, where aa and bb are integers to be determined. [2]
c
Justify why the rule T(n)=n2T(n) = n^2 must contain an n2n^2 term by referring to the geometric structure of Figure nn. [2]
Question diagram

Solutions

Questions 5-372

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 372.

+368 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade