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 also be written in the form of a percentage or fraction. The probability of likely event B is often written as P(B). Here P shows the possibility and B show 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.

Though probability started with a gamble, in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc., it has been used carefully.

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 there is same chance 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 occurs} ⁄ {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 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 coin is fair, then the probability of getting either a head or a tail is 0.5. 

According to binomial concept 

So the probability of getting 10 heads in a row 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 outcome → 5 Heads {H,H,H,H,H}

This can occur only ONCE!

Thus, required outcome  =1  

Probability (5 Heads) = (1⁄2)⁵ = 1/32