### All Algebra II Resources

## Example Questions

### Example Question #11 : Calculating Probability

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

**Possible Answers:**

**Correct answer:**

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.

Our final answer is

.

### Example Question #12 : Calculating Probability

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

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

`

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

If A and B are two independent events (the outcome of one does not affect the outcome of the other), the following formula is used to calculate the overall probability.

The event of flipping a coin and rolling a die are independent events since flipping a coin does not affect the probability of rolling a certain number on the die, and vice versa.

The probability of flipping a heads on a coin is .

The probability of rolling a factor of 6 on a six-sided die (1,2,3,6) is .

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