What is the probability of getting exactly six tails if you flip a coin eight times.

Probability is a part of mathematics that deals with the possibility of happening of events. It is to forecast that what are the possible chances that the events will occur or the event will not occur. The probability as a number lies between 0 and 1 only and can also be written in the form of a percentage or fraction. The probability of likely event A is often written as P(A). Here P shows the possibility and A shows the happening of an event. Similarly, the probability of any event is often written as P(). When the end outcome of an event is not confirmed we use the probabilities of certain outcomes—how likely they occur or what are the chances of their occurring.

To understand probability more accurately we take an example as rolling a dice:

The possible outcomes are — 1, 2, 3, 4, 5, and 6.

The probability of getting any of the outcomes is 1/6. As the possibility of happening of an event is an equally likely event so there are same chances of getting any number in this case it is either 1/6 or 50/3%.

Formula of Probability

Probability of an event, P(A) = (Number of ways it can occur) ⁄ (Total number of outcomes)

Types of Events

• Equally Likely Events: After rolling dice, the probability of getting any of the likely events is 1/6. As the event is an equally likely event so there is same possibility of getting any number in this case it is either 1/6 in fair dice rolling.
• Complementary Events: There is a possibility of only two outcomes which is an event will occur or not. Like a person will play or not play, buying a laptop or not buying a laptop, etc. are examples of complementary events.

If a coin is flipped 8 times, then what is the probability of getting 4 heads?

Solution:

Use the binomial distribution directly. Let us assume that the number of heads is represented by x  (where a result of heads is regarded as success) and in this case X = 4

Assuming that the coin is unbiased, you have a probability of success ‘p’(where p is considered as success) is 1/2 and the probability of failure ‘q’ is 1/2(where q is considered as failure). The number of trials is represented by the letter ’n’ and for this question n = 8.

Now just use the probability function for a binomial distribution:

P(X = x) = nCxpxqn-x

Using the information in the problem we get

P(X = 4) = (8C4)(1/2)4(1/2)4

= 70 × 1/16 × 1/16

= 70/256

= 35/128

Hence, the probability of flipping a coin 8 times and getting heads 4 times is 35/128.

Similar Questions

Question 1: What is the probability of flipping a coin 20 times and getting 5 heads?

Answer:

Each coin can either land on heads or on tails, 2 choices.  

(According to the binomial concept)

This gives us a total of 220 possibilities for flipping 20 coins.

Now how many ways can we get 5 heads? This is 20 choose 5, or (20C5)  

This means our probability is (20C5)/220 = 15504⁄1048576 ≈ .01478

Question 2: What is the probability of 4 heads in 4 coins tossed together.?

Solution:

4 coin tosses. This means,

Total observations = 16(According to binomial concept)  

Required outcome → 4 Heads {H,H,H,H}

This can occur only ONCE!

Thus, required outcome = 1  

Probability (4 Heads) = (1⁄2)4 = 1/16

All ACT Math Resources

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.

All ACT Math Resources

ACT Math Tutoring in Top Cities:

Atlanta ACT Math Tutoring, Austin ACT Math Tutoring, Boston ACT Math Tutoring, Chicago ACT Math Tutoring, Dallas Fort Worth ACT Math Tutoring, Denver ACT Math Tutoring, Houston ACT Math Tutoring, Kansas City ACT Math Tutoring, Los Angeles ACT Math Tutoring, Miami ACT Math Tutoring, New York City ACT Math Tutoring, Philadelphia ACT Math Tutoring, Phoenix ACT Math Tutoring, San Diego ACT Math Tutoring, San Francisco-Bay Area ACT Math Tutoring, Seattle ACT Math Tutoring, St. Louis ACT Math Tutoring, Tucson ACT Math Tutoring, Washington DC ACT Math Tutoring

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

What is the probability of flipping a coin 8 times?

What are the odds of getting tails 8 times in a row?

What is the probability of obtaining 6 tails in a row when flipping a coin?

What are the chances of getting tails 6 times in a row?