We have two coins, a and b. for each toss of coin a, we obtain heads with probability 1/2 ; for each toss of coin b, we obtain heads with probability 1/3 . all tosses of the same coin are independent. we toss coin a until heads is obtained for the first time. we then toss coin b until heads is obtained for the first time with coin b. the expected value of the total number of tosses is:

The expected value is 5.

Step-by-step explanation:

As we can see, X=Y+Z. Then, by the linearity of the expected value operator, we have that

Observe that Y and Z have countable sets of outcomes (1,2,3,....) then,

,

,

Then:

Observe that, by the geometric series formula:

Therefore

Finally, E(X)=E(Y)+E(Z)=2+3=5.

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.