A group of individuals containingbboys andggirls is lined up in a randomorder; that is, each of the (g+b)! permutations is assumed to be equally likely. What is the probability that the person in theithposition (1≤i≤b+g) isa girl?

g/(b + g)

Step-by-step explanation:

We are told the group of individuals contain b number of boys and g number of girls.

Now the number of ways of selecting 1 girl out of g number of girls is;

gC1 = g!/(g - 1)! = (g × (g - 1)!)/(g - 1)!

(g - 1)! will cancel out to give;

gC1 = g

Now, since total number of boys and girls is b + g, and we have chosen one girl out, the remaining number of people will be; b + g - 1.

Thus, number of ways to arrange the remaining people will be;

(b + g - 1)!

Now, the probability that the person in the ith position (1 ≤ I ≤ b+g) is a girl will be;

(gC1 × (b + g - 1)!)/(b + g)!

We know that gC1 = g from earlier derivation.

Expanding this gives;

[g(b + g - 1) × (b + g - 2)!]/[(b + g) × (b + g - 1) × (b + g - 2)!]

(b + g - 1) × (b + g - 2)! will cancel out to give;

g/(b + g)

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560