Question

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.​

Answer 1

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 $(n(S))$ = 4 + 3 = 7
• Total number of males $(n(M))$ = 4

The probability of sending a male member $(P(M))$ = $\displaystyle \frac{n(M)}{n(S)}$

                                                                                    = $\displaystyle \frac{4}{7}$

On the 2nd day:

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

• Total number of all members $(n(S))$ = 7 - 1 = 6
• Total number of males $(n(M))$ = 4 - 1 = 3

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

                                                                                         = $\displaystyle \frac{3}{6}$

Sending both males on both days $(P(M\cap M))$ = $P(M)\times P(M|M)$

                                                                              $\displaystyle=\frac{4}{7} \times\frac{3}{6}$

                                                                              $\displaystyle=\bf\frac{2}{7}$