(a) let {a1, a2} be a partition of a sample space and let b be any event. state and prove the law of total probability as it applies to the partition {a1, a2} and the event b.
there are two coins in a box; one coin is a fair coin, and the other is a biased coin thatcomes up heads 75 percent of the time. fiona chooses a coin at random and tosses it.
(b) what is the probability that the chosen coin flips heads? (hint: the law of totalprobability.)
(c) given that the chosen coin flips heads, what is the conditional probability that it wasthe biased coin? (hint: bayes’ theorem.)
(d) given that the chosen coin flips tails, what is the conditional probability that it wasthe biased coin?

0.625

Step-by-step explanation:

Given that {A1, A2} be a partition of a sample space and let B be any event. State and prove the Law of Total Probability as it applies to the partition {A1, A2} and the event B.

Since A1 and A2 are mutually exclusive and exhaustive, we can say

b) P(B) = P(A1B)+P(A2B)

Selecting any one coin is having probability 0.50. and A1, A2 are events that the coins show heads.

c) Using Bayes theorem

conditional probability that it wasthe biased coin

=

d) Given that the chosen coin flips tails,the conditional probability that it was the biased coin=

homozygous. one is homozygous, while two is heterozygous.

step-by-step explanation:

one of the most important purposes of surface treatment is to alter surface properties according to the requirement of specific applications. for example, hydrophobic coating has been utilized on windshield and eyeglasses. gold atom monolayer on substrate has become a popular surface bioconjugation strategy.