The probability of event a is x, and the probability of event b is y. if the two events are independent, which of these conditions must be true?
a. p(b|a) = y
b. p(a|b) = y
c. p(b|a) = x
d. p(a and b) = x + y
p(a and b) = x

p(a) y

The correct options are:

      A.  P(B|A) = y

We know that when two events A and B are independent.

Then,

P(A∩B)=P(A)×P(B)

As we are given:

P(A)=x and P(B)=y

Hence,

P(A∩B)=xy

Also,

Hence, P(A|B)=x

and similarly,

Hence,

  P(B|A)=y

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.