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

Conditional probability

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Probability of compound events
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:conditional_probability/5448/


Example 1.

A dodecahedron is a regular polyhedron bounded by 12 regular pentagons. On each face, write one of the numbers from 1 to 12, which are not repeated.




  • We roll two numbered dodecahedra at the same time. What is the probability of the event A that the sum of the numbers on the two upper faces is a prime number, less than or equal to 5?


  • One numbered dodecahedron is rolled 20 times. What is the probability of the event B that in these 20 repetitions of the experiment, the number 7 will appear on the top face exactly 3 times? Round the result to three decimal places.


  • Make the edge length of the dodecahedron equal to . Calculate the sum of the lengths of all the edges and the area of ​​this dodecahedron.

    
Example 2.

10 physicists and 8 chemists gathered at the congress of natural scientists. Only one physicist is named Francis, only one chemist is Klemen. The participants of the congress will choose from their ranks a 5-member presidency, in which 3 physicists and 2 chemists must be. In how many ways can they do this if there are no other constraints?


Calculate the probability of the event A that at least one of the previously mentioned persons (physicist Francis or chemist Klemen) will be in the presidency, if the members of the presidency are chosen randomly from physicists and chemists.