Fair coin is tossed three times. What is the probability that all three tosses land on heads, given that:(a) the first toss lands on heads(b) at least one toss lands on heads.

(a) The probability that all three tosses land on heads given that the 1st toss lands on Heads is .

(b) The probability that all three tosses land on heads given that at least one toss lands on heads is .

Step-by-step explanation:

The sample space of tossing 3 coins is:

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} = 8 outcomes.

(a)

The sample space such that the 1st toss lands on Heads is:

S₁ = {HHH, HHT, HTH, HTT} = 4 outcomes.

The probability that all three tosses land on heads given that the 1st toss lands on Heads is:

P (3 Heads | 1st toss is Heads) =

Thus, the probability that all three tosses land on heads given that the 1st toss lands on Heads is .

(b)

The sample space such that at least one toss lands on heads is:

S₂ = {HHH, HHT, HTH, THH, HTT, THT, TTH} = 7 outcomes

The probability that all three tosses land on heads given that at least one toss lands on heads is,

P (3 Heads | At least 1 Heads)

Thus, the probability that all three tosses land on heads given that at least one toss lands on heads is .

answer: about 22.67

step-by-step explanation:

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.