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# What is the probability of getting 10 heads in 20 flips? – GeeksforGeeks

What is the probability of getting 10 heads in 20 flips ? probability is a part of mathematics that deals with the possibility of happening events. It is to forecast 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 besides be written in the form of a share or fraction. The probability of probable event B is much written as P ( B ). here P shows the possibility and B show the happen of an event. similarly, the probability of any event is much written as P ( ). When the end consequence of an event is not confirmed we use the probabilities of certain outcomes—how likely they occur or what are the chances of their occur. Though probability started with a gamble, in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, and so forth, it has been used cautiously. 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 probably event there is like casual of getting any number, in this case, it is either 1/6 or 50/3 %. Formula of Probability

probability of an event = { Number of ways it can occur } ⁄ { total number of outcomes } P ( A ) = { Number of ways A occur } ⁄ { total count 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 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.

### What is the probability of getting 10 heads in 20 flips?

Solution:

Each coin can either land on heads or on tails, 2 choices. ( According to binomial concept ) This gives us a total of 220 possibilities for flipping 20 coins. now how many ways can we get 10 heads ? This is 20 choose 10, or ( 20C10 ) This means our probability is ( 20C10 ) /220= 184756⁄1048576 ≈ .1762

### Similar Questions

Question1: What is the probability of 10 heads in 10 coins tossed together.? Solution:

If the mint is bonny, then the probability of getting either a head or a fag end is 0.5.
According to binomial concept
So the probability of getting 10 heads in a quarrel is 0.510≈0.00098 which is 1 in 1024 .

Question 2: What is the probability of 5  in 5 coins tossed together.? Solution:

5 coin tosses. This means, total observations = 25 ( According to binomial concept ) Required consequence → 5 Heads { H, H, H, H, H } This can occur only once ! therefore, required result =1 Probability ( 5 Heads ) = ( 1⁄2 ) 5 = 1/32

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