Probability And Polynomial Help?

Question

1.) If I have two die what's the probability of getting P(rolling a 4 or lower)? T

 

2.) What's the second term in the polynomial: (2x-1)^5 ? 

 

a.  -160x^5
b. -16x^4
c. -80x^4
d. -10x^4
e. -64x^4

 

Thank you! 

Answer 1

Question 1 is unclear. are you talking about rolling a four or lower as the sum of the two dice?  In which case it is 1/6.

 

Six possibilities (1,1),(1,2),(1,3),(2,1),(2,2), and (3,1) out of 36.

 

Or of rolling a 4 or less on either die?  Try:

 1 - Probability (rolling only 5 or 6) = 1 - (1/3)(1/3) = 1 - 1/9 = 8/9

 

 

 

Question 2 is rapidly done using Pascal's Triangle, the coefficients of a fifth order equation are 1,5,10,10,5,1.

 

So the second term is 5a⁴b = 5(2)⁴(-1) = -5(16x⁴) = -80x⁴