Suppose three coins are tossed. What's the probability of having exactly 1 tail, 3 tails, or all the same?
To calculate the probability of each scenario, we first need to determine the total number of possible outcomes when tossing three coins. Each coin can either land as heads or tails, so there are 2 possibilities for each coin flip. Since we have three independent coin flips, the total number of outcomes is 2 * 2 * 2 = 8.
1. Probability of getting exactly 1 tail:
To find the number of favorable outcomes, we need to determine how many different ways we can get exactly 1 tail. Out of the three coins, there are three possible positions where the tail could occur (first coin, second coin, or third coin). For each position, we have 2 options (either head or tail). Therefore, the total number of favorable outcomes is 3 * 2 = 6.
Probability = Favorable Outcomes / Total Outcomes = 6 / 8 = 3/4 = 0.75
2. Probability of getting exactly 3 tails:
There is only one way to obtain exactly 3 tails since all three coins need to land on tails.
Probability = Favorable Outcomes / Total Outcomes = 1 / 8 = 1/8 = 0.125
3. Probability of getting all the same (either all heads or all tails):
There are two favorable outcomes to get all the same (HHH or TTT).
Probability = Favorable Outcomes / Total Outcomes = 2 / 8 = 1/4 = 0.25
So, the probability of getting exactly 1 tail is 0.75, the probability of getting exactly 3 tails is 0.125, and the probability of getting all the same is 0.25.