What is the probability of flipping a coin eight times and receiving at least one head?

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If you flip a coin 3 times, what are the odds that the coin will be heads all three times?

Correct answer:

Explanation:

If you flip a coin, the chances of you getting heads is 1/2. This is true every time you flip the coin so if you flip it 3 times, the chances of you getting heads every time is 1/2 * 1/2 * 1/2, or 1/8.

What is the probability of getting a sum of four when rolling two six-sided dice?

Correct answer:

Explanation:

The sample space for rolling two six-sided dice , since each die has sides.

There are three ways to roll a four.

The probability of rolling a four is given by the number of outcomes that produce a four divided by the total number of outcomes.

A bag contains 3 green marbles, 5 red marbles, and 9 blue marbles.

What is the probability of drawing a red marble?

Correct answer:

Explanation:

The probability of drawing a red marble is .

The total number of marbles  is , so there are  possible outcomes.  of these possible outcomes are red marbles, so the probability of a red marble out of any marble is .

In a certain lottery, ten balls are numbered #1 through #10.  Two winning balls will be drawn without replacement.

Billy plays the lottery and picks the numbers 9 and 10.

What is the probability Billy Bob will have two winning numbers?

Possible Answers:

1/90

1/50

2/95

1/45

1/100

Explanation:

(1/10)(1/9) = 1/90

In a lottery, ten balls are numbered #1 through #10.  Two winning balls will be drawn without replacement.

Billy plays the lottery and picks the numbers 9 and 10.

What is the probability that Billy has no winning numbers? (Round to the nearest one percent.)

Explanation:

The correct answer is 62%, obtained from (8/10) (7/9) = 0.62222

A fair coin is tossed 2 times.

When flipping a coin twice, what is the probability of getting one heads and one tails? Without regard to order. I.e., either the heads or the tails could appear first.

Explanation:

There are 4 possible outcomes for the event {HH, HT, TH, TT}. Two of these four outcomes include exactly one heads and one tails. 

Thus the solution is 2/4 = 1/2 = 0.5

With a pair of standard six-sided dice, what is the probability of getting a sum of less than five OR at least ten?

Correct answer:

Explanation:

Probability is a fraction between 0 and 1. The denominator is the total number of possible outcomes and the numerator is the total number of desired outcomes. For two dice, the total number of ways to roll the dice is 36 (6 on the first die can go with any of the 6 on the second die)

The following outcomes result in a sum of less than 5:  {1, 1}  {1, 2}  {1, 3}  {2, 1}  {2, 2}  {3, 1}, for 6 possible outcomes

The following outcomes result in a sum of at least 10:  {4, 6}  {5, 6}  {5, 5}  {6, 6}  {6, 5}  {6, 4} for 6 possible outcomes

Since we are looking for a sum of less than five OR a sum of at least ten, we sum up the total number of desired outcomes

So the probability of getting less than five or at least ten will be 12/36, or 1/3

There are 6 pink marbles, 3 green marbles, and 5 white marbles in a bag; if one marble is taken out, what is the probability that the marble is pink?

Correct answer:

Explanation:

There are 6 pink marbles out of 14 total, which reduces to 3/7.

A fair coin is flipped three times. What is the probability that the outcome is heads all three times?

Correct answer:

Explanation:

There are 8 possible sequences that can occur given this scenario, listed as {HHH, HHT, HTT, HTH, THT, THH, TTH, TTT} 

Only one element in this set is the desired outcome of 3 heads. So we get 1/8 is our probability.

Another way to look at this problem is to consider that the probability of flipping heads once is 1/2, so the probability of flipping heads 3 times consecutively is 1/2 * 1/2 * 1/2 = 1/8

A single die is rolled and one coin is flipped. 

What is the probability of getting a number less than 4 on the die and a heads on the coin?

Correct answer:

Explanation:

To get a number less than 4 on a die, 3/6 is the probability. To get a heads is a 1/2 chance.

So, since both events are independent, multiply the two probabilities together to get your answer.

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What is the probability of flipping a coin 8 times and getting all heads?

What is the probability of getting at least one head?

How many possibilities are there if you flip a coin 8 times?

What is the probability of flipping a coin 8 times and getting heads 2 times?