Examples Using Tossing a Coin Probability Formulas

Example 1: Find the probability of getting a head when a coin is tossed.

Solution: 

Total Outcomes of Coin Toss = {H, T} (2)

Favorable Outcome = {H} (1)

Probability = Favourable Outcome/ Total Outcome

P(H) = 1/2 = 0.5

So there is a 50% chance of getting a head when a coin is tossed.

Example 2: Find the probability of getting at least 1 tail when two coins are tossed.

Solution: 

Let B be the event of getting at least 1 tail if two coins are tossed.

Total Outcomes of two coin toss = {(H, T), (T, H), (T, T), (H, H)} = 4

Number of Favorable Outcomes = {(H, T), (T, H), (T, T)} = 3

Probability of Getting at least 1 tail if 2 coins are tossed = P(B)

 P(B) = (Number of Favorable Outcomes)/(Total Possible Outcomes)

P(B) = 3/4 = 0.75

So there are 75% of chance of getting at least 1 tail when two coins are tossed.

Example 3: Find the probability of getting head and tail at the same time when a single coin is tossed.

Solution: 

The outcome of a coin toss is, {H, T}

We see that there is no outcome when the Head and Tail are achieved simultaneously.

Thus, the probability of getting head and tail simultaneously is Zero.

Example 4: Find the probability of getting three heads when 3 coins are tossed at the same time.

Solution: 

Let E be the event of getting three heads when 3 coins are tossed.

Total Possible Outcomes of three coin toss ({HHH}, {HHT}, {HTH}, {THH}, {HTT}, {TTH}, {THT}, {TTT})

Total Number of Possible Outcomes = 8

Favorable Outcomes = {HHH}

Number of Favorable Outcomes = 1

As per the Coin Toss Probability Formula,

P(E) = (Number of Favorable Outcomes)/(Total Number of Possible Outcomes)

P(E) = 1/8 = 0.125

So, there is a 12.5% chance of getting all 3 heads when 3 coins are tossed.

Example 5: Find the probability of getting at least two heads when 3 coins are tossed at the same time.

Solution: 

Let F be the event of getting at least two heads when 3 coins are tossed.

Total Possible Outcomes of three coin toss ({HHH}, {HHT}, {HTH}, {THH}, {HTT}, {TTH}, {THT}, {TTT})

Total Number of Possible Outcomes = 8

Favorable Outcomes = ({HHT}, {HTH}, {THH}, {HHH})

Number of Favorable Outcomes = 4

As per the Coin Toss Probability Formula,

P(F) = (Number of Favorable Outcomes)/(Total Number of Possible Outcomes)

P(F) = 4/8 
        = 1/2 = 0.5

So, there is a 50% chance of getting at least two heads when 3 coins are tossed.

Also Check:

• Probability Theory
• Experimental Probability
• Chance and Probability
• Probability Theorems
• Events in Probability

Tossing a Coin Probability: Coin Toss Probability Formula is the formula that tells us the probability of finding the head or tail in a coin toss. Before learning more about the coin toss probability formula, let’s learn more about, What is Probability. Probability is a branch of Mathematics that tells how likely an event occur. We define it as, the possibility of happening an event. Its value always lies between 0 (zero) to 1 (one) where 0 indicates an impossible event and 1 indicates a certain event. 

Now let’s learn more about the coin toss probability formula and examples in detail in this article. The following image shows an unbiased coin that has an equal probability of landing both heads and tails.