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There are 4 male and 3 female members in a family. A member is sent for 2 days continuously in certain work without repetition. Represent the probability for getting both days male in a tree diagram.​

Respuesta :

Answer:

Please find the attached picture for the tree diagram.

Step-by-step explanation:

To find the probability for getting both days male, we can work this way:

Let:

  • A = event of sending a family member on the 1st day
  • B = event of sending a family member on the 2nd day
  • M = male member
  • M' = female member

On the 1st day:

  • Total number of all members [tex](n(S))[/tex] = 4 + 3 = 7
  • Total number of males [tex](n(M))[/tex] = 4

The probability of sending a male member [tex](P(M))[/tex] = [tex]\displaystyle \frac{n(M)}{n(S)}[/tex]

                                                                                    = [tex]\displaystyle \frac{4}{7}[/tex]

On the 2nd day:

Since there is no repetition, then this event is a dependent event

  • Total number of all members [tex](n(S))[/tex] = 7 - 1 = 6
  • Total number of males [tex](n(M))[/tex] = 4 - 1 = 3

The probability of sending a male member [tex](P(M|M))[/tex] = [tex]\displaystyle \frac{n(M)}{n(S)}[/tex]

                                                                                         = [tex]\displaystyle \frac{3}{6}[/tex]

Sending both males on both days [tex](P(M\cap M))[/tex] = [tex]P(M)\times P(M|M)[/tex]

                                                                              [tex]\displaystyle=\frac{4}{7} \times\frac{3}{6}[/tex]

                                                                              [tex]\displaystyle=\bf\frac{2}{7}[/tex]

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