a. Provide two independent events that you know the probability of. b. Explain how you know these events are independent. c. Find the probability that they both occur. a. Provide two dependent events. b. Explain how you know these events are dependent. c. Explain why these dependent events might require a different method for calculating the probability of both events occurring.

Explained below.

Step-by-step explanation:

(1)

(a)

Consider the independent events A and B as follows:

A = a coin toss results in Heads

B = a 3 is rolled on a fair dice.

P (A) = 1/2

P (B) = 1/6

(b)

Consider the experiment where a coin is tossed and a dice is rolled.

The outcome of the coin toss is not affected by the outcome of the dice rolling.

And vice-versa.

Thus, the events A and B are not dependent on each other.

(c)

Compute the probability of A and B both occurring together as follows:

; Since A and B are independent.

Thus, the probability of A and B both occurring together is 1/12.

(2)

(a)

Consider the dependent events A and B as follows:

A bag of marbles consist of 6 red, 5 blue and 4 green marbles. Two marbles are selected without replacement.

A = a green marble is selected first

B = a red marble is selected second.

P (A) = 4/15

P (B) = 6/14

(b)

Consider the experiment where two marbles are selected from the bag without replacement and their color is noted.

Since the marbled are selected without replacement, the selection of the second marble is dependent upon the first.

That is, after the first selection, the total number of marbles in the bag would be reduced by 1. Hence affecting the probability of selection of the second marble.

Thus, the events A and B are dependent on each other.

(c)

Compute the probability of A and B both occurring together as follows:

Thus, the probability of A and B both occurring together is 4/35.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.