What is the probability of flipping a coin six times and receiving at least one tail?

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 7 times, then what is the probability of getting 6 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 = 6

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 = 7.

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The ratio of successful events A = 63 to the total number of possible combinations of a sample space S = 64 is the probability of 1 tail in 6 coin tosses. Users may refer the below solved example work with steps to learn how to find what is the probability of getting at-least 1 tail, if a coin is tossed fix times or 6 coins tossed together. Users may refer this tree diagram to learn how to find all the possible combinations of sample space for flipping a coin one, two, three or four times.

Solution
Step by step workout
step 1 Find the total possible events of sample space S
S = {HHHHHH, HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HHTTTT, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTHTTT, HTTHHH, HTTHHT, HTTHTH, HTTHTT, HTTTHH, HTTTHT, HTTTTH, HTTTTT, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THHTTT, THTHHH, THTHHT, THTHTH, THTHTT, THTTHH, THTTHT, THTTTH, THTTTT, TTHHHH, TTHHHT, TTHHTH, TTHHTT, TTHTHH, TTHTHT, TTHTTH, TTHTTT, TTTHHH, TTTHHT, TTTHTH, TTTHTT, TTTTHH, TTTTHT, TTTTTH, TTTTTT}

S = 64

step 2 Find the expected or successful events A
A = {HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HHTTTT, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTHTTT, HTTHHH, HTTHHT, HTTHTH, HTTHTT, HTTTHH, HTTTHT, HTTTTH, HTTTTT, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THHTTT, THTHHH, THTHHT, THTHTH, THTHTT, THTTHH, THTTHT, THTTTH, THTTTT, TTHHHH, TTHHHT, TTHHTH, TTHHTT, TTHTHH, TTHTHT, TTHTTH, TTHTTT, TTTHHH, TTTHHT, TTTHTH, TTTHTT, TTTTHH, TTTTHT, TTTTTH, TTTTTT}

A = 63

step 3 Find the probability
P(A) = Successful Events/Total Events of Sample Space
= 63/64

= 0.98
P(A) = 0.98

0.98 is the probability of getting 1 Tail in 6 tosses.

Unfortunately, the footnote ends there, so there's not much in the way of detail about what these restrictions are or how long they'd remain in effect in a potential post-acquisition world. Given COD's continued non-appearance on Game Pass, you've got to imagine the restrictions are fairly significant if they're not an outright block on COD coming to the service. Either way, the simple fact that Microsoft is apparently willing to maintain any restrictions on its own ability to put first-party games on Game Pass is rather remarkable, given that making Game Pass more appealing is one of the reasons for its acquisition spree.

The irony of Sony making deals like this one while fretting about COD's future on PlayStation probably isn't lost on Microsoft's lawyers, which is no doubt part of why they brought it up to the CMA. While it's absolutely reasonable to worry about a world in which more and more properties are concentrated in the hands of singular, giant megacorps, it does look a bit odd if you're complaining about losing access to games while stopping them from joining competing services.

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

There is a probability of 0.5 for each tail, and since each coin toss is independent, we can multiply that by itself six times in order to find the probability that each toss results in tails. Therefore, the probability of at least one head is as follows. So, there is a 98.44% probability of getting at least one head.

What is the probability of getting at least one tail when tossing six fair coins?

Probability of occurring at least one tail=1−641=6463.

What is the probability of getting a tail and a 6?

Summary: The probability of getting a tail and a six when a coin is tossed and a cube is rolled is 1/12.

What are the possible outcomes of flipping a coin 6 times?

Because each flip of the coin offers two possibilities and we are flipping 6 times, the multiplication principle tells us that there will be: 2 · 2 · 2 · 2 · 2 · 2=26 = 64 possible outcomes.