twenty-five percent of all death are caused by diseases of the heart Ischemic heart disease accounts for 16.4% of all death and heart failure for 2.3% choose one death at random. What is the probability that it is from ischemic heart disease given that it was from heart disease. choose two death at random. what is the probability atleast one is from heart disease
To find the probability that a randomly chosen death is from ischemic heart disease, given that it was from heart disease, we can use conditional probability.
First, we need to find the probability of choosing a death that is from heart disease. From the given information, we know that 25% of all deaths are caused by heart diseases. Therefore, the probability of choosing a death from heart disease is 0.25.
Next, we need to find the probability that a chosen death from heart disease is specifically from ischemic heart disease. According to the given data, ischemic heart disease accounts for 16.4% of all deaths caused by heart diseases. So, the probability of choosing a death from ischemic heart disease, given that it was from heart disease, is 0.164.
Hence, the probability that a randomly chosen death is from ischemic heart disease, given that it was from heart disease, is 0.164/0.25 = 0.656 or 65.6%.
Now, let's move on to the second part of the question: choosing two deaths at random and finding the probability that at least one is from heart disease.
To solve this, we can calculate the complementary probability, which is the probability that neither of the chosen deaths is from heart disease, and then subtract it from 1.
The probability that the first randomly chosen death is not from heart disease is 1 - 0.25 = 0.75. Similarly, the probability that the second randomly chosen death is not from heart disease is also 0.75.
Since these events are independent, the probability that neither of the chosen deaths is from heart disease is calculated by multiplying the individual probabilities: 0.75 * 0.75 = 0.5625.
Finally, the probability that at least one of the two chosen deaths is from heart disease is 1 - 0.5625 = 0.4375 or 43.75%.
So, the probability that at least one of two chosen deaths is from heart disease is 0.4375 or 43.75%.