GCSE Maths Higher

The free GCSE Maths Higher diagnostic

6 questions, about 5 minutes. We name the exact AQA misconception losing you marks -- not “you need more practice”, the specific pattern -- and point you at the targeted lesson that fixes it.

No signup needed. Designed around AQA. Year 10 and Year 11.

GCSE Maths Higher Diagnostic: Combined & conditional probabilityQuestion 1 of 6

There are two bags of beads.

Bag A contains 3 Yes beads and 2 No beads. Bag B contains 1 Yes bead and 9 No beads.

One bead is picked at random from each bag.

450 people each pick one bead from Bag A and one bead from Bag B.

Work out the expected number of people who pick a Yes bead from both bags.

*(Show your working.)*

A two-stage probability tree. Bag A is chosen first with branches Yes (probability 3/5) and No (probability 2/5). From each node, Bag B is chosen with branches Yes (probability 1/10) and No (probability 9/10). Outcome labels show the combined events. The Yes-Yes branch probability is marked with a question mark.Bag ABag B3/5Yes2/5No1/10Yes9/10No1/10Yes9/10NoYes, YesYes, NoNo, YesNo, No
The free GCSE Maths Higher diagnostic