Of people who died in the US in recent years, 86% were white, 12% were black, and 2% were Asian. (This ignores a small number of deaths among other races.) Diabetes cause 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. The probability that a randomly chosen death is a white who died of diabetes is about:
A) .107, B.) .030 C.) .024
Part 2
Using the information in the previous exercise, the probability that a randomly chosen death was due to diabetes is about:
A) .107 B) .030 C) .024
Probability that both/all events would occur is found by multiplying the individual probabilities.
.86 * .028 = ?
Either-or probability is found by adding the individual probabilities.
(.86 * .028) + (.12 * .044) + (.02 * .035) = ?
To find the probability that a randomly chosen death is a white person who died of diabetes, we first need to find the probability that a randomly chosen death is a white person and the probability that a randomly chosen death was due to diabetes among whites.
Given that 86% of people who died in the US were white, the probability that a randomly chosen death is a white person is 0.86.
Given that 2.8% of deaths among whites were due to diabetes, the probability that a randomly chosen death was due to diabetes among whites is 0.028 (2.8% expressed as a decimal).
To find the probability that a randomly chosen death is a white person who died of diabetes, we multiply the two probabilities:
0.86 * 0.028 = 0.02408
Therefore, the probability that a randomly chosen death is a white person who died of diabetes is approximately 0.024 or 2.4%.
Now, to find the probability that a randomly chosen death was due to diabetes, we need to calculate the probability for each race individually and then sum them up.
Using the percentages provided:
- 86% of deaths were white, and 2.8% of white deaths were due to diabetes, which gives 0.86 * 0.028 = 0.02408 as the contribution from white deaths.
- 12% of deaths were black, and 4.4% of black deaths were due to diabetes, which gives 0.12 * 0.044 = 0.00528 as the contribution from black deaths.
- 2% of deaths were Asian, and 3.5% of Asian deaths were due to diabetes, which gives 0.02 * 0.035 = 0.0007 as the contribution from Asian deaths.
Summing up the contributions from each race, we get:
0.02408 + 0.00528 + 0.0007 = 0.03006
Therefore, the probability that a randomly chosen death was due to diabetes is approximately 0.030 or 3.0%.
So the answers to the two questions are:
A) 0.024 for the probability that a randomly chosen death is a white person who died of diabetes.
B) 0.030 for the probability that a randomly chosen death was due to diabetes.
Part 1: To find the probability that a randomly chosen death is a white who died of diabetes, we need to multiply the probability of being white (86%) by the probability of dying from diabetes given that they are white (2.8%).
Probability = 0.86 * 0.028 = 0.02408
Therefore, the probability is approximately 0.024.
Answer: C) 0.024
Part 2: To find the probability that a randomly chosen death was due to diabetes, we need to calculate the weighted average probability of dying from diabetes across different races.
Multiply the probability of being white (86%) by the probability of dying from diabetes given that they are white (2.8%). Then do the same for blacks (12% * 4.4%) and Asians (2% * 3.5%). Finally, sum up these three probabilities.
Probability = (0.86 * 0.028) + (0.12 * 0.044) + (0.02 * 0.035) = 0.024 + 0.00528 + 0.0007 = 0.02998
Therefore, the probability is approximately 0.030.
Answer: B) 0.030