Question

1.Find the indicated probability.

​In one town, 39% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary.

2. What is the probability that a card randomly drawn from a standard deck of 52 cards is NOT a king?

3. Fred and Ed each have a bag of candy that contains a lemon drop (L), a cherry drop (C), and an orange drop (O). Each takes out one piece from their bag and eats it. What is the sample space of the possible pairs of candies eaten?

4. Event A has a 0.3 probability of occurring and event B has a 0.4 probability of occurring. A and B are independent events. What is the probability that neither A or B occurs?

5. Solve the problem.

How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from?

Answer 1

@Vocaloid or @dude pls help w/ this whenever you're online

Answer 2

1. 39% of the population is "democrat"
The probability of randomly selecting a democrat is 39% right?
The probability of selecting another democrat is also 39% right?
You can draw a tree diagram:

Answer 3

You want both of them to be democrat

in the tree-diagram the only option where both of them are democrats is this path over here

You multiply the probability together. (39% x 39%) and that's your answer

Answer 4

2. There are 52 cards. That's your sample space/population

There are 4 cards that are kings so there are 48 cards that aren't kings.
That's 48/52.

You can also do it like this:
Probability that a card drawn isn't a king = 100% - Probability that a card drawn is king
Probability of a card drawn that is king = 4/52
1 - (4/52) will give you the same answer.

Answer 5

3. The sample space is all possible outcomes.
Both of them have a bag with 3 different items.

Here is all possible outcomes:

Answer 6

notice how some of them are the same thing since the order does not matter here.

So the sample space is AA AB AC BB BC CC
That's 6

Answer 7

4. For 2 independent events. You can use this formula: P(A and B) = P(A) x P(B)

You can also use this formula: P(A or B) = P(A) + P(B) - P(A and B)

Solve for P(A or B)
Once you know that then you can find out 1 - P(A or B) and that's the probability of neither A or B occuring.

Answer 8

5. Think of it like this:
_ _ _ _ _ _

There's 8 people to choose from for the first place
7 people to choose from for 2nd place
6 people to choose from for 3rd place
blah blah blah
and 3 people to choose from for 6th place

8 7 6 5 4 3

Multiply them together
8 x 7 x 6 x 5 x 4 x 3 = Your answer

You'll learn a formula for this when you study permutations and combinations

Answer 9

@Vocaloid for #4 the answer would be 0.12? that's what I got

Answer 10

0.12 is the probability that A and B both happen but the question is asking the probability that **neither** happen

so you are given P(A) = 0.3 and P(B) = 0.4

P(not A) must therefore be 1 - 0.3
and P(not B) must therefore be 1 - 0.4

and P(neither A nor B) = P(not A) * P(not B)

Answer 11

@Vocaloid 0.42?

Answer 12

good