Explain the answers in sufficient details ie show the work a

ace? What is the probability of drawing a red ace? Are these events (\"ace\" and \"red\") mutually exclusive? Are they independent? e. List two events that are mutually exclusive for a single draw from a deck of cards. What is the probability of drawing a red f. king? What is the probability of drawing a face card in hearts? Are these two events mutually exclusive? Are they independent? 20. The human genome is composed of the four DNA nucleotides: A, T, G, and C. Some regions of the human genome are extremely G-C rich (i.e., a high proportion of the DNA nucleotides there are guanine and cytosine). Other regions are relatively A-T rich (i.e., a high proportion of the DNA nucleotides there are adenine and thymine). Imagine that you want to compare nucleotide sequences from two regions of the

Solution

a) Let we have two regions, Region1 and Region2.

It is given that 60% nucleotides in 1st region is A&T (30% each) and remaining 40% is of G&C nucleotides(20% each). Probability of the nucleotides in Region1:

Similarly for region2, Probability of the nucleotides in Region2:

Probability of getting both are same nucleiods, we must multiply the individual probabilities.

Probability of getting both has type A nucleoids=P(A1)*P(A2)

Probability of getting both has type T nucleoids=P(T1)*P(T2)

Probability of getting both has type G nucleoids=P(G1)*P(G2)

Probability of getting both has type C nucleoids=P(C1)*P(C2)

Required probability=P(A1)*P(A2)+ P(T1)*P(T2)+ P(G1)*P(G2)+ P(C1)*P(C2)

                                     =0.25

b)

It is given that two regions are independent. To find probability to select three nucleoids sequence (triplets) from each of the two regions are same.

All combinations made with the nucleoids A, T, G and C taking three at a time 4C3.

The number of all combinations of 4 things taken 3 at a time is 4C3=4

Possible selections are ATG, TGC, GCA and CAT

Suppose we get outcome as ATG from Region1, so Probability of getting it is

Nucleotides	P (N)
A1	0.2
T1	0.2
G1	0.3
C1	0.3