In maths, probability is a chance of occurrence of random events. Tossing a coin is an example of probability. When you toss a coin, the outcome may be head or tail. But if you toss 2 coins simultaneously, the sample space will have 4 possibilities. Here we will learn about the outcomes of coin toss probabilities along with the examples.
Coin Toss Probability
We generally see a coin toss before the commencement of a match to take the decision between two teams. The result of tossing a coin experiment is head or tail. Obtaining the result as the head is 50% and the tail is also 50%. If you toss one coin, there are only two possible outcomes.
The probability occurrence of an event is always measured between 0 and 1. 1 indicates the occurrence of an event and 0 represents the unlikely occurrence of an event probability.
Number of possible outcomes = 2
Number of outcomes to get head = 1
Probability of getting head = ½
Probability of an event = \(\frac { Number of favourable outcomes }{ Total number of possible outcomes } \)
Probability of Tossing Two Coins
We can find the probability of tossing 2 coins at a time or tossing 3 coins probability. Here we will learn the complete details of two coin-tossing probabilities. When we toss two coins simultaneously then the possible outcomes are two heads, two tails, one head and one tail. The sample space S = {(H, H), (H, T), (T, H), (T, T). Here ‘H’ represents the head and ‘T’ represents the tail.
The total number of outcomes = 2² = 4
Then, the probability of getting 2 tails = \(\frac { 1 }{ 4 } \). As the sample space as only 1 time and the total number of outcomes are 4.
Solved Examples on Probability of Flipping 2 Coins
Example 1:
If two coins are flipped randomly. Find the probability of
(i) getting two heads
(ii) getting one tail
(iii) getting no tail
Solution:
If two coins are tossed, then the sample space is S = {HH, TT, HT, TH}
(i) getting two heads
The number of times, we get two heads = 1
So, probability of getting two heads P(E1) = \(\frac { 1 }{ 4 } \)
(ii) getting one tail
The number of times, we can get one tail = 2 = {HT, TH}
So, probability of getting one tail P(E2) = \(\frac { 2 }{ 4 } \) = ½
(iii) getting no tail
The number of times, we can get no tail = 1 = {HH}
So, probability of getting no tail P(E3) = \(\frac { 1 }{ 4 } \)
Example 2:
When 2 coins are tossed, find the probability of
(i) getting atmost 1 head
(ii) getting 1 head and 1 tail
(iii) getting at least 1 tail
Solution:
If two coins are tossed, then the sample space is S = {HH, TT, HT, TH}
(i) getting atmost 1 head
Event of getting atmost 1 head = {TT, TH, HT} = 3
Therefore, P(getting atmost 1 head) = \(\frac { 3 }{ 4 } \)
(ii) getting 1 head and 1 tail
Event of getting 1 head and 1 tail = { TH, HT} = 2
Therefore, P(getting 1 head and 1 tail) = \(\frac { 2}{ 4 } \) = ½
(iii) getting at least 1 tail
Event of getting at least 1 tail = {TT, TH, HT} = 3
Therefore, P(getting at least 1 tail) = \(\frac { 3 }{ 4 } \)
FAQ’s on Probability of Flipping Two Coins
1. What is the sample space of tossing 2 coins?
The sample space of tossing two coins is {HH, TT, HT, TH}.
2. How to find the probability of two coins?
The formula to find the probability of two coins = \(\frac { Number of favourable outcomes }{ 4 } \). Place the values to get the answer.
3. When two coins are tossed what is the probability of getting tails for both the coins?
When two coins are tossed, the number of favourable outcomes = 4. The chance of getting two tails = \(\frac { 1 }{ 4 } \)
4. What is the probability of getting 2 heads when the two coins are tossed simultaneously?
When two coins are tossed, the number of favourable outcomes = 4. The probability of getting two heads = \(\frac { 1 }{ 4 } \)