Answer to Question #105240 in Statistics and Probability for Michael Henry

Question

Brian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type.

Suppose a recent study shows that 28% of adults have blood type A, 21% of adults have blood type B, 34% of adults have blood type AB, and 17% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities.

What is the probability that Brian and Jennifer share the same blood type? Give your answer as a decimal, precise to at least two decimal places.

Answer 1

$P(same\;type)=P(A)P(A)+P(B)P(B)+P(AB)P(AB)+P(O)P(O)=\\ =0.28*0.28+0.21*0.21+0.34*0.34+0.17*0.17=0.267.$