Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

22.) A life insurance company examined the medical records of 1,0051,005 women who died in 20102010 and discovered that 300300 of the women died from causes related to cancer. Moreover, 473473 of the 1,0051,005 women had at least one parent who suffered from cancer, and, of these 473473 women, 225225 died from causes related to cancer.\newlineLet \newlineP(A)P(A) be the probability that a given woman from the total group died of cancer, and let \newlineP(AB)P(A\mid B) be the probability that a given woman died of cancer, given that she had at least one parent who suffered from cancer. Calculate \newlineP(AB)P(A)\frac{P(A\mid B)}{P(A)}.\newline(A) 0.6270.627\newline(B) 30030000\newline(C) 30030011\newline(D) 30030022\newline(E) 30030033

Full solution

Q. 22.) A life insurance company examined the medical records of 1,0051,005 women who died in 20102010 and discovered that 300300 of the women died from causes related to cancer. Moreover, 473473 of the 1,0051,005 women had at least one parent who suffered from cancer, and, of these 473473 women, 225225 died from causes related to cancer.\newlineLet \newlineP(A)P(A) be the probability that a given woman from the total group died of cancer, and let \newlineP(AB)P(A\mid B) be the probability that a given woman died of cancer, given that she had at least one parent who suffered from cancer. Calculate \newlineP(AB)P(A)\frac{P(A\mid B)}{P(A)}.\newline(A) 0.6270.627\newline(B) 30030000\newline(C) 30030011\newline(D) 30030022\newline(E) 30030033
  1. Calculate P(A)P(A): Calculate P(A)P(A), the probability that a given woman from the total group died of cancer.P(A)=Number of women who died of cancerTotal number of womenP(A) = \frac{\text{Number of women who died of cancer}}{\text{Total number of women}}P(A)=3001005P(A) = \frac{300}{1005}
  2. Calculate P(AB)P(A\mid B): Calculate P(AB)P(A\mid B), the probability that a given woman died of cancer given that she had at least one parent who suffered from cancer.\newlineP(AB)=Number of women who died of cancer and had at least one parent who suffered from cancerTotal number of women who had at least one parent who suffered from cancerP(A\mid B) = \frac{\text{Number of women who died of cancer and had at least one parent who suffered from cancer}}{\text{Total number of women who had at least one parent who suffered from cancer}}\newlineP(AB)=225473P(A\mid B) = \frac{225}{473}
  3. Calculate the ratio: Calculate the ratio (P(AB))/(P(A))(P(A\mid B))/(P(A)).(P(AB))/(P(A))=(225473)/(3001005)(P(A\mid B))/(P(A)) = (\frac{225}{473}) / (\frac{300}{1005})
  4. Simplify the ratio: Simplify the ratio by multiplying the numerator and denominator by the reciprocal of the denominator.\newline(P(AB))/(P(A))=(225473)×(1005300)(P(A\mid B))/(P(A)) = (\frac{225}{473}) \times (\frac{1005}{300})
  5. Perform the multiplication: Perform the multiplication to find the ratio.\newline(P(AB))/(P(A))=(225×1005)/(473×300)(P(A\mid B))/(P(A)) = (225 \times 1005) / (473 \times 300)\newline(P(AB))/(P(A))=226125/141900(P(A\mid B))/(P(A)) = 226125 / 141900
  6. Simplify the fraction: Simplify the fraction to get the final answer. P(AB)P(A)=2261251419001.594\frac{P(A|B)}{P(A)} = \frac{226125}{141900} \approx 1.594

More problems from Solve proportions: word problems