Final answer:
The probability of landing tails can be found by subtracting the probability of landing heads from 1. Since the given coin has a probability of 0.4 of landing heads, the probability of landing tails would be 1 - 0.4 = 0.6.
Step-by-step explanation:
In probability theory, the probability of an event is a measure of the likelihood that the event will occur. For a coin toss, where there are two possible outcomes (heads or tails), the sum of the probabilities for all possible outcomes must equal 1. If the probability of landing heads is given as 0.4 for an unfair coin, we can find the probability of landing tails by subtracting the probability of heads from 1.
�(Tails)=1−�(Heads)
P(Tails)=1−P(Heads)
In this formula,
�(Tails)
P(Tails) represents the probability of landing tails, and
�(Heads)
P(Heads) represents the probability of landing heads. The subtraction from 1 accounts for the fact that there are only two possible outcomes, and their probabilities must add up to 1.
Substituting the given probability into the formula:
�(Tails)=1−0.4=0.6
P(Tails)=1−0.4=0.6
So, the probability of landing tails on the unfair coin is
0.6 0.6 or 60%
60%. This means that if the coin is tossed numerous times, we would expect it to land on tails approximately 60% of the time, given its unfair nature with a 0.4 probability of landing heads. This calculation follows the fundamental principles of probability, ensuring that the sum of probabilities for all possible outcomes is equal to 1.