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mathematics UK Year 12 Mathematics (AS)
 
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Independent events and the multiplication law

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:independent_events_and_the_multiplication_law/5447/


Example 1.

There are girls and boys in a class. A three-member committee is to be chosen to prepare for a program. Calculate the probability that both sexes will be represented on this committee .

    
Example 2.

In a basket are three oranges, two grapefruits and five tangerines. If we randomly select two fruits, what is the probability that they will both be tangerines?

    
3.

There were 16 persons: 4 married couples, 5 single men and 3 single women at the party. For the board game we randomly select 2 persons. Calculate the probability of events:


  • A - the chosen persons are a married couple.

  • B - selected persons are singles and of different sexes.

    
4. Please restore this question

We make new words from the letters of the word TRIGLAV. We use all the letters each time and each one only once.


  • How many different words can we make?


  • How many such words are there in which all the consonants stand together?


  • What is the probability of the event A ​​that a randomly composed word starts with the letter T and ends with the letter V?

    
5.

Alex, Bettty, Maria, Nina and Thiago randomly line up for tickets. What is the probability of the event A that the girls are standing at the beginning of the line?

    
6.

The seller has 15 tickets in the bag: 5 winning and 10 empty. We buy 4 randomly selected tickets. Calculate the probability of events:

  • A - at least one purchased lottery ticket will win,

  • B - two purchased tickets will be winning, two will not.

    
7.

The teacher will randomly divide tests of two types among 12 students (among them Drake, Jones and Milan, others have different names): 6 students will write a test A, 6 student test B. What is the probability that all three (Drago, Jaka and Milan) will write the test A? What is the probability that at least one of the three will write the test B?

    
8.

From the group of boys and girls we randomly select persons. Calculate the probability of the event that three boys and one girl will be selected.

    

9.

We randomly choose three gifts from five books, three toys and two packets of candy. Calculate the probability of an event that we selected one book, one toy, and one pack of candies.