Final answer:
The probability of at least 2 tails occurring when a fair coin is tossed 27 times is approximately 0.999999940395355.
Step-by-step explanation:
To find the probability of at least 2 tails occurring when a fair coin is tossed 27 times, we can use the complementary probability. The complementary probability is the probability of the opposite event occurring. In this case, the opposite event is the probability of getting 0 or 1 tail. So, we need to find the probability of getting 0 tail and 1 tail and subtract it from 1.
Step 1: Probability of getting 0 tail.
The probability of getting a tail on a fair coin toss is 1/2. Since we want to find the probability of 0 tails, we need to find the probability of getting a head on all 27 tosses. This can be calculated as (1/2)^27.
Step 2: Probability of getting 1 tail.
The probability of getting exactly 1 tail can be calculated by multiplying the probability of getting a tail once (1/2) and the probability of getting a head for the remaining 26 tosses ((1/2)^26). So, the probability of getting 1 tail is (1/2)*(1/2)^26.
Step 3: Calculate the complementary probability.
The complementary probability is calculated by subtracting the probability of getting 0 tail and 1 tail from 1. So, the probability of at least 2 tails occurring is 1 - [(1/2)^27 + (1/2)*(1/2)^26].
Step 4: Simplify the expression.
This can be done using a calculator. The probability comes out to be approximately 0.999999940395355.