Answer:
5/9
Step-by-step explanation:
At the beginning, there are 5 + 5 = 10 people to choose from. After one woman is chosen, that number goes down to 10 - 1 = 9 people. 5 men are still left to choose from, so there is a 5/9 chance at least one man will be selected as the other committee member.
Answer:
5/7
Step-by-step explanation:
Number of women = 5
Number of men = 5
2 people is to be chosen to form a committee.
Let as assume
A : At least one man was chosen
B : At least one woman was chosen
A ∩ B : Exactly one man and one woman was chosen
P(B) = Exactly one woman was chosen + Two women was chosen
[tex]P(B)=\dfrac{^5C_1\times ^5C_1+^5C_0\times ^5C_2}{^{10}C_2}\Rightarrow \frac{5\times 5+1\times 10}{45}=\frac{35}{45}=\frac{7}{9}[/tex]
[tex]P(A\cap B)=\dfrac{^5C_1\times ^5C_1}{^{10}C_2}\Rightarrow \frac{5\times 5}{45}=\frac{25}{45}=\frac{5}{9}[/tex]
We need to find the probability at least one man was chosen given at least one woman was chosen.
[tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}[/tex]
[tex]P(\frac{A}{B})=\dfrac{\frac{5}{9}}{\frac{7}{9}}[/tex]
[tex]P(\frac{A}{B})=\frac{5}{7}[/tex]
Therefore, the required probability is 5/7.
