The Laplace High School basketball team has a probability of 1/2 of winning a game, independent of previous games. The probability

that, in a sequence of 8 games, the team wins two of its last four

games and four of its eight games can be expressed in lowest

terms as 7. What is a + b?

a= 1/2 and b= 1/2

Step-by-step explanation:

The given probability can be expressed in the form of binomial expansion  where a= p and b= q

Therefore a= 1/2 and b= 1/2

For n= 8 trials the binomial expansion can be written as

[ p+q] ^n = [ 1/2+1/2]^8

=(1/2)^0(1/2)^8 +8C1(1/2)^7(1/2)+8C2(1/2)^6(1/2)^2+8C3(1/2)^5(1/2)^3+8C4(1/2)^4(1/2)^4+8C5(1/2)^3(1/2)^5+8C6(1/2)^2(1/2)^6+8C7(1/2)(1/2)^7+8C8(1/2)^0(1/2)^8

=

1(1/2)^0(1/2)^8 +8(1/2)^7(1/2)+28(1/2)^6(1/2)^2+56(1/2)^5(1/2)^3+70(1/2)^4(1/2)^4+56(1/2)^3(1/2)^5+28(1/2)^2(1/2)^6+8(1/2)(1/2)^7+1(1/2)^0(1/2)^8

=

1/(2)⁸ { 1+ 8+28+56+70+56+28+8+1}

= 1/(2)⁸ {256}

= 1

The total probability is always 1.

Also P+q= 1

1/2+1/2= 1

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.