1 of 8 0-day streak

Multi-stage probability, multiplication and total probability

Question 1 of 8

No calculator

A trial selects one component from a tray at each stage

The initial category counts, in the branch order shown, are typeA = 7, typeB = 6

At each stage, choose uniformly at random from the individual items currently in the container

The trial has 2 stages: stage 1 and stage 2. After each selection, the item is returned before the next stage

The ordered terminal outcomes form the sample space \(S\). Let \(E\) be the event that the ordered outcome is (typeB, typeA)

If needed, scroll sideways to follow each complete path

Read stages from left to right. A ? marks a branch probability to calculate. Terminal labels show the complete ordered outcomes

(a)1 mark

Which calculation plan matches the probability of the required path and event?

Multiply the probabilities of the different selected paths together

Use multiplication down the selected 2-stage path to find its probability

Add the branch probabilities along each selected path, then combine the resulting values

(b)2 marks

Fill the labelled branch and terminal-path probabilities exactly

Pr(first outcome is typeB) Pr(typeA, typeA)

Find the exact probability of the ordered path \(\mathrm{typeB},\, \mathrm{typeA}\)

Path probability

Format: exact fraction