A single coin is tossed 300 times. Heads were observed 180 times. What is the long-run relative frequency of tails? Express the answer in decimal form.
The relative frequency of tails in the long run is simply the number of times tails would be expected to come up if the coin were tossed an infinite number of times. Since this is a fair coin (assuming no information to the contrary), we know that the probability of getting tails on a single toss is 0.5. Therefore, the expected number of tails in 300 tosses is 0.5 times 300, or 150.
Since we observed heads 180 times, we must have seen tails 300 - 180 = 120 times. Thus, the relative frequency of tails is 120/300 = 0.4, or 40%.
To find the long-run relative frequency of tails, we need to calculate the ratio of the number of tails observed to the total number of tosses.
The number of tails can be calculated by subtracting the number of heads observed from the total number of tosses:
Number of tails = Total number of tosses - Number of heads observed
Number of tails = 300 - 180
Number of tails = 120
Now, we can calculate the long-run relative frequency of tails by dividing the number of tails by the total number of tosses:
Long-run relative frequency of tails = Number of tails / Total number of tosses
Long-run relative frequency of tails = 120 / 300
Long-run relative frequency of tails = 0.4
Therefore, the long-run relative frequency of tails is 0.4.