3. A magical four-sided die is rolled twice. Let S be the sum of the resultsof the two rolls. We are told that the probability that S = k is proportional to k, for k = 2, 3, . . . , 8, and that all possible ways that a given sum k can arise are equallylikely. Construct an appropriate probabilistic model and find the probability of gettingdoubles.

P(S=k) = (1/35)k

8/21

Step-by-step explanation:

P(S=k) is proportional to k

P(S=k) = ck

Total probability is 1

k = 2,3 8

Sum of all probabilities =

2c + 3c + 4c + 5c + 6c + 7c + 8c = 1

35c = 1

c = 1/35

P(S=k) = (1/35)k, where k = 2,3,...8

P(1&1):

P(S=2) = 2/35

P(2&2):

P(S=4)/3 = (1/3)(4/35) = 4/105

Because for S=4: (1,3) (2,2) (3,1) and all are equally likely

P(3&3):

P(S=6)/3 = (1/3)(6/35) = 2/35

Because for S=6: (2,4) (3,3) (4,2)

P(4&4):

P(S=8) = 8/35

P(getting doubles = 2/35 + 4/105 + 2/35 + 8/35 = 40/105 = 8/21

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.