In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females and 12 of the juniors are males. if a student is selected at random, find the probability of selecting the following.

a. a junior or a female
b. a senior or a female
c. a junior or a senior

a) 0.857

b) 0.571

c) 1

Step-by-step explanation:

Based on the data given, we have

The probability of each union of events is obtained by summing the probabilities of the separated events and substracting the intersection. I will abbreviate female by F, junior by J, male by M, senior by S. We have

Note that a student cant be Junior and Senior at the same time, so the probability of the combined event is 0. The probability of the union is 1 because every student is either Junior or Senior.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1