Answer:
Explanation:
one tail?
The probability of getting tails on a single flip of a fair coin is 1/2, and the same holds for heads. We can use these probabilities to find the probabilities for each of the scenarios:
a) Getting all tails:
The probability of getting tails on the first flip is 1/2, and the same holds for each subsequent flip since the coin is fair and the outcomes are independent. Therefore, the probability of getting all tails is (1/2) x (1/2) x ... x (1/2) = (1/2)^12 = 0.0002441406 (rounded to 4 decimal places).
b) Getting all heads:
By the same reasoning as in part a), the probability of getting all heads is also (1/2)^12 = 0.0002441406 (rounded to 4 decimal places).
c) Getting at least one tail:
The complement of getting at least one tail is getting no tails, i.e., getting all heads. Therefore, the probability of getting at least one tail is 1 minus the probability of getting all heads:
P(at least one tails) = 1 - P(all heads) = 1 - (1/2)^12 = 0.9997558594 (rounded to 4 decimal places).