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If a coin is tossed 5 times, what is the probability that it will always land on the same side?

  • Last Updated : 20 Oct, 2021

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 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 so there are some chances 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 a dice the probability of getting any of the likely events is 1/6. As the event is an equally likely event so there is some 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 tossed 5 times, what is the probability that it will always land on the same side?

Solution:

Let us assume that after flipping 5 coins we get 5 heads in result 

5 coin tosses. This means,

Total observations = 25 (According to bionominal concept)

Required outcome → 5 Heads {H,H,H,H,H}



This can occur only ONCE!

Thus, required outcome =1

Now put the probability formula  

Probability (5 Heads) =(1⁄2)5 = 1⁄32

Similarly, for the condition with all tails, 

the required outcome will be 5 Tails {T,T,T,T,T}

Probability of occurrence will be the same i.e. 1⁄32

Hence, the probability that it will always land on the same side will be, 1⁄32 + 1⁄32 = 2⁄32 = 1⁄16

Similar Questions

Question 1: What is the probability of flipping 5 coins on the Tails side?

Solution:



5 coin tosses. This means,

Total observations = 25 (According to binomial concept)

Required outcome → 5 Tails {T,T,T,T,T}

This can occur only ONCE!

Thus, required outcome =1

Now put the probability formula  

Probability (5 Tails) = 1⁄25 = 1⁄32

Question 2: What is the probability of flipping 4 coins on the Head’s side?

Solution:

4 coin tosses. This means,

Total observations = 24 (According to binomial concept)

Required outcome → 4 Heads {H,H,H,H}

This can occur only ONCE!

Thus, required outcome = 1

Now put the probability formula

Probability (4 Heads) = 1⁄24 = 1⁄16

Question 3: What is the probability of flipping 3 coins on the Tails side?

Solution:

3 coin tosses. This means,

Total observations = 23 (According to binomial concept)

Required outcome → 3 Tails {T,T,T}

This can occur only ONCE!

Thus, required outcome = 1 

Now put the probability formula 

Probability (3 Tails) = 1⁄23 = 1⁄8

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