Question

a family has 8 girls and 4 boys. a total of 3 children must be chosen to speak on behalf of their family at a local benefit. what is the probability that no girls and 3 boys will be chosen

Answer 1

Answer: The required probability that no girls and 3 boys will be chosen is
`(1)/(55).`

Step-by-step explanation: Given that a family has 8 girls and 4 boys. a total of 3 children must be chosen to speak on behalf of their family at a local benefit.

We are to find the probability that no girls and 3 boys will be chosen.

Let, S denotes the sample space for the experiment of choosing 3 children and E be the event that no girls and 3 boys will be chosen.

Then, we have

`n(S)=^(8+4)C_3=^(12)C^3=(12!)/(3!(12-3)!)=(12*11*10*9!)/(3*2*1*9!)=4*5*11=220,\\\\\\n(E)=^4C_3=(4!)/(3!(4-3)!)=(4*3!)/(3!*1)=4.`

Therefore, the probability of event E will be

`P(E)=(n(E))/(n(S))=(4)/(220)=(1)/(55).`

Thus, the required probability that no girls and 3 boys will be chosen is
`(1)/(55).`

Answer 2

Answer
1/55

Step-by-step explanation
The probability of an event is a chance of it happening. It is calculated as;
Probability =(fouvarable outcome)/(total outcome)
Since we are finding the probability of no girl will be chosen, it is like finding the probability of choosing 3 boys.
The probability of choosing the first boy =4/12
The probability of choosing the second boy =3/11
The probability of choosing the third boy =2/10
The probability of choosing the 3 boys will be,
=4/12×3/11×2/10
=24/1320
=1/55