Suppose there are two species of panda bear. Both are equally common in the wild

Question

Suppose there are two species of panda bear. Both are equally common in the wild and live
in the same places. They look exactly alike and eat the same food, and there is yet no genetic assay
capable of telling them apart. They differ however in their family sizes. Species A gives birth to twins
10% of the time, otherwise birthing a single infant. Species B births twins 20% of the time, otherwise
birthing singleton infants. Assume these numbers are known with certainty, from many years of field
research.
Now suppose you are managing a captive panda breeding program. You have a new female panda
of unknown species, and she has just given birth to twins. What is the probability that her next birth
will also be twins?
2H2. Recall all the facts from the problem above. Now compute the probability that the panda we
have is from species A, assuming we have observed only the first birth and that it was twins.

Explanation / Answer

Both are equally common in the wild and live in the same places so probability of each will be same

i.e. P(A)=P(B)=1/2=0.5

P(twins|A)=0.1

and P(twins|B)=0.2

P(twins)=P(A)*P(twins|A)+P(B)*P(twins|B)=0.5*0.1+0.5*0.2=0.15

so, probability that her next birth will also be twins=0.15

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.