Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. (We will ignore the small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. What is the probability that a randomly chosen death was due to diabetes? (Round your answer to three decimal places.)

To three decimal place = 0.030

Step-by-step explanation:

Let probability of death in white p (WH) = 86%

Let probability of death in black p (B) = 12%

Let probability of death in Asian p (A) = 2%

Probability of death caused by diabetes among white will be 2.8% of p (WH) = 0.86 x 0.028 = 0.02408

Probability of death caused by diabetes among black will be 4.4% of p (B) = 0.12 x 0.044 = 0.00528

Probability of death caused by diabetes among Asian will be 3.5% of p (A) = 0.02x 0.035 = 0.0007‬

If a sample is chosen and the cause is diabetes then the probability will be

Probability of death caused by diabetes among white or Probability of death caused by diabetes among black or Probability of death caused by diabetes among Asian

0.02408 + 0.00528 + 0.0007 = 0.03006

To three decimal place = 0.030