In Mr ERIZ's class, the probability of student who likes Mathematics subject is 0.5 and the probability who likes both Mathematics and Statistics subjects is 0.25.

If one student is chosen at random, what is the probability that this student likes Statistics given that he/she also like Mathematics subject?

(2 marks)

If the probability of students who like Statistics is 0.45, are the events 'like Mathematics subject' and 'like Statistics subject' independent? Justify your answer.

(4 marks)

Are the events 'likes Mathematics' and 'likes Statistics' mutually exclusive? Justify your answer.

Question 2 1 pts Consider the following relation R on a set A R = { (a,a) (a,b) (b,a) (b,b) (b.c) (c,c) } Consider the following statements Stat 1 : R is an equivalence relation Stat 2: R is not an equivalence relation because it is not transitive Stat 3: R is not an equivalence relation because it is not symmetric Stat 4 : Adding just one ordered pair to R can make the new relation equivalence relation Choose the correct statements a) Stat 1 is True and Stat 4 is true b)Stat 2 is true c)Stat 4 is false d)Stat 3 is false O b)Stat 2 is true d)Stat 3 is false O c)Stat 4 is false a) Stat 1 is True and Stat 4 is true36. Put the following steps in Jak/STAT signaling in order. opnsfoxe omni lot arts to doinW.eE ( ) Jak receptors dimerize and cross-phosphorylate each other ( ) STATs are translocated to the nucleus Sc10- ( ) STATs are phosphorylated ( ) Phosphorylated STATs dimerize with each other ( ) STATs bind to phosphotyrosines using SH2 domains ( ) STATs bind to DNA to regulate transcription of target genes srigis O- ( ) ligand binds receptor