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?

8000/531441

Step-by-step 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!

step-by-step explanation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: