Question

Six people are randomly selected in succession, with replacement, from a class containing 25 men and 20 women. What is the probability of obtaining the sequence 1, 0, 0, 0, 1, 1, where 1 indicates a man was chosen and 0 indicates a woman was chosen?

Answer 1

8000/531441

Explanation:

With 25 men and 20 women that means there are 45 people in total. This means the ratio of men to total is 25:45 which we can reduce to 5:9 which means there is a 5/9 chance we would pick a man if we just chose one person. The ratio of women to total is 20:45 which we can reduce to 4:9 meaning there is a 4/9 chance we would pick a women if we just choice one person. When finding probability of multiply things happening we multiply and because this situation is with replacement. So we will multiply

(5/9)(4/9)(4/9)(4/9)(5/9)(5/9)=8000/531441

I hope this helps and please don't hesitate to ask if there is anything still unclear!