Matched: 78% of 1,200 = 0.78 × 1,200 = 936
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- Total change = 900 − 1,200 = −300 meters over 10 years
- Rate = −300 ÷ 10 = −30 meters per year (descending)
- A linguist compares two dialects and finds that 78% of core vocabulary matches. If the corpus contains 1,200 cognates, how many do not match?
- Not matched: 1,200 − 936 = 264
- #### 264Question: An epidemiologist models the spread of a virus where each infected person has a $\frac{1}{3}$ chance of transmitting it to a contact. What is the probability that exactly 2 out of 4 contacts become infected?
- Solution: The probability follows a binomial distribution with parameters $n = 4$ (trials) and $p = \frac{1}{3}$ (success probability). The formula for exactly $k$ successes is $\binom{n}{k} p^k (1-p)^{n-k}$. For $k = 2$:
