Question

A student council has nine officers, of which six are girls and three are boys. If two officers are chosen at random to attend a meeting with the principal, what is the probability that the first officer chosen is a girl and the second is a boy? please help

Answer 1

The probability that the first officer chosen is a girl and the second is a boy is 1/4.

Step-by-step explanation:

To find the probability that the first officer chosen is a girl and the second is a boy, we can use the concept of dependent events.

When the first officer is chosen, there will be 6 girls left out of a total of 9 officers.

Therefore, the probability of selecting a girl as the first officer is 6/9.

After the first officer is chosen, there will be 3 boys left out of 8 officers. So, the probability of selecting a boy as the second officer is 3/8.

Since the events are dependent, we can multiply the probabilities of each event to get the probability of both events happening.

So, the probability of the first officer being a girl and the second officer being a boy is (6/9) * (3/8) = 1/4, which can also be written as 0.25 or 25%.

Answer 2

Answer:
`(1)/(4)`

Step-by-step explanation:

Given

Student council has 6 girls and 3 boys

If two person chosen at random

Probability that first officer is girl and second is a boy

`=\text{Probability of choosing a girl officer}* \text{Probability of choosing a boy officer}`

`=(^6C_1)/(^9C_1)* (^3C_1)/(^8C_1)`

`=(6)/(9)* (3)/(8)`

`=(1)/(4)`