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mathematics UK Year 12 Mathematics (AS)
 
Solved problems for the chapter:
 

Experiments, events and outcomes

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:experiments%2C_events_and_outcomes/5445/


Example 1.

There are 50 tickets in the bag, 40 of which bring prizes and the remaining 10 do not.


  • One ticket is randomly drawn from the bag. Calculate the probability of the event A ​​that the chosen ticket brings a prize.

  • Two tickets are randomly drawn from the bag at the same time. Calculate the probability B of the event that both selected tickets bring a prize.

  • Three tickets are randomly drawn from the bag at the same time. Calculate the probability of the event C that at least one chosen ticket brings a prize.

    
Example 2.

Write the sample space of the throw of two coins.

    
3.

We throw a normal die and a die that has the numbers 2,4,6,8,10,12. What are all the possible outcomes if we calculate the absolute value of the difference of the numbers on both dice?

    
4.

We roll two fair dice. Draw a table of the sample space of the sum of the outcomes.

    
5.

Write down all the possible outcomes and the tree diagram for throwing two coins.

    
6.

We have five numbered beads in the bag. We draw three beads without returning the drawn balls. Write all possible outcomes of the experiment.

    
7.

We create two set of 5 cards with each set having numbers from 1 up to 5 and add them up. In how many ways can we get:


  • 10

  • number in between 6 and 9

  • Prime number

    
8.

We roll three dice. How many ways can we get the sum of 10,13,16?

    

9.

Three fair dice are tossed. What are the possible outcomes:


  • if one falls exactly on one cube


  • if one falls on at least one cube?