a consonant? Sjngle coin is tossed 300 times. Heads were observe 180 times. What is the long run relative frequency of tails . Express in decimal form

Answer 1

There are a couple of ways to approach this problem, but one possible method is to use the fact that the long run relative frequencies of heads and tails add up to 1. Therefore, if we know the relative frequency of heads, we can subtract it from 1 to get the relative frequency of tails. Specifically,

Relative frequency of heads = number of heads observed / total number of tosses
= 180 / 300
= 0.6

Relative frequency of tails = 1 - relative frequency of heads
= 1 - 0.6
= 0.4

Therefore, the long run relative frequency of tails is 0.4, or 40% in decimal form. This means that if we continue to toss the coin many times (i.e., in the long run), we expect to observe tails about 40% of the time and heads about 60% of the time. Note that this is based on the assumption that the coin is fair (i.e., has an equal chance of landing heads or tails on each toss). If the coin is biased in some way (e.g., it is weighted), then the long run relative frequencies may be different.