There are $3$ men and $2$ women in a Grampanchayat. A committee of two is formed. Find the probability of P is the event that the committee should contain at least one woman.

Open in App

Solution

$\begin{matrix} a t l e a s t o n e w o m e n p o s s i b l e c o n d i t i o n a r e^{2} C_{1} \times^{3} C_{1} = 2 \times 3 = 6^{2} C_{2} \times^{3} C_{0} = 1 \times 1 = 1 6 + 1 = 7 S a m p l e s p a c e^{2} C_{1} \times^{3} C_{1} +^{2} C_{2} \times^{3} C_{0} +^{3} C_{2} \times^{2} C_{0} = 6 + 1 + 3 = 10 o b a b i l i t y o f g r a m p a n c h a y a t a t l e a s t 1 w o m e n i s = \frac{7}{10} \end{matrix}$

Suggest Corrections

Similar questions

Q. There are

3

men and

2

women in a Grampanchayat. A committee of two is formed. Find the probability of Q is the event that committee should contain one man and one woman.

Q. There are 3 men and 2 women. A 'Gramswachhatta Abhiyan' committee of two is to be formed:
P is the event that the committee should contain a least one woman.
Q is the event that the committee should contain one man and one woman.
R is the event that there should not be a woman in the committee.

Q. There are

3

men and

2

women. a 'Gramswachhatta Abhiyan' committee of two is to be formed :

P

is event that the committee should contain at least one woman.

Q

is event that the committee should contain one man and one women.

R

is the event there should not be a women in the committee.

S

is the sample space.

Which of the following options is correct?

Q. A group contains

10

men and

4

women. Three members committee is formed which must contain at least on woman. Find the probability that the committee so formed has more women and men.

Write a sample space $S$ and number of sample points $n (S)$ for the following experiments. Also write events $A, B, C$ in the set from and write $n (A), n (B)$ and $n (C)$ .

From three men and two women, environment committee of two person to be formed.
Condition for event $A :$ There must be at least one woman member.
Condition for event $B :$ One man, one woman committee to be formed.
Condition for event $C :$ There should not be a woman member.

Join BYJU'S Learning Program

There are 3 men and 2 women in a Grampanchayat. A committee of two is formed. Find the probability of P is the event that the committee should contain at least one woman.

atleastonewomenpossibleconditionare2C1×3C1=2×3=62C2×3C0=1×1=16+1=7Samplespace2C1×3C1+2C2×3C0+3C2×2C0=6+1+3=10obabilityofgrampanchayatatleast1womenis=710

There are $3$ men and $2$ women in a Grampanchayat. A committee of two is formed. Find the probability of P is the event that the committee should contain at least one woman.