# Algebra II : Algebra II

## Example Questions

### Example Question #11 : Calculating Probability

If I flip a coin twice, what's the probability it lands on tails twice?

Explanation:

Let's list all possible outcomes.

We have H T, H, H, T T, T H.

There are four possible outcomes so that represents the denominator.

Since we are looking for two tails, we only have one possible outcome which is the numerator.

### Example Question #12 : Calculating Probability

What's the probability I pick a face card in a standard  card deck?

Explanation:

There are three face cards which are J Q K.

Next, there are four suits for every face card which gives us a total of  cards we are looking for.

Finally, since there are  cards in a deck, we do a fraction of .

There is no answer given however if we divide top and bottom by  we get an answer of

.

### Example Question #13 : Calculating Probability

What's the probability of a die rolled once and shows a prime number?

Explanation:

In a die, there are six sides numbered

.

Prime numbers are numbers with a factor of one and itself.

The prime numbers are .

We have three outcomes and it's divided over six possible outcomes.

So our fraction is  or

### Example Question #14 : Calculating Probability

Bob picks a random card in a standard  card deck. After keeping the card, he takes another card and keeps it again. What's the probability that he has a pair in his hand?

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Explanation:

In a standard deck, there are thirteen kind of cards from . There are four suits. To have a pair is to have the same kind of card but with different suit. Since we are looking for any pair, the first card Bob picks is anything so the probability is .

Because he keeps the card, we have  cards remaining. To get that same card, there are only  of them left in the deck. So the chance of getting a pair becomes .

We don't have this choice but if we divide both sides by  we get .

### Example Question #15 : Calculating Probability

There are four red socks, five blue socks, eight white socks, and two yellow socks, What's the probability of picking a blue or yellow sock?

Explanation:

When we see or, we must add probabilities. Since there are  socks and we are interested in blue or yellow, we add those totals up.

There are  blue or yellow socks to get.

Our fraction now becomes

.

### Example Question #16 : Calculating Probability

Two cards are drawn from a standard  deck of cards without replacement. What's the probability of drawing an ace and a three in that order?

Explanation:

To draw an ace first, our chances are  or .

Since there is no replacement, we now have  cards.

To draw the three, our chances are .

Because it's two conditions that need to be satisfied, we multiply

.

### Example Question #17 : Calculating Probability

If an exam, there is only one right answer and four wrong answers, what's the probability of getting the one question right out of two?

Explanation:

The probability of getting a question right is .

The probability of getting a question wrong is .

We are tempted to multiply both fractions to get an answer of . The issue is we don't know which question needs to be right.

So in this case, we multiply that fraction by  to get an answer of .

### Example Question #11 : Calculating Probability

If the probability of raining today is , what's the probability it won't rain today?

Explanation:

If probability of raining is , that means the probability of not raining is .

Probability must add up to  because we are certain of all possible events which are raining and not raining.

By doing the math, our answer is

.

### Example Question #19 : Calculating Probability

There are five letters . I must choose two with replacement. What's the probability I pick a  and  but not necessarily in that order?

Explanation:

The probability of picking any letter is .

The question doesn't specify an order as there are two ways of picking .

We can have  first then  or we can have  first, then .

So probability of picking  in no order is

### Example Question #20 : Calculating Probability

Given a fair two-sided coin and a fair six-sided die, what is the probability of flipping a heads and rolling a factor of 6?