SAJC Check your Understanding_Probability_teacher

Check your Understanding (Probability) Section 1: Venn Diagram 1. Kesamet Junior College celebrated Staff Fruits Day, where 150 teachers received a free fruit each. The gender of the teachers and types of fruits each teacher received were recorded in the table shown below. Male Female Apple 12 28 Banana 55 32 Orange 8 15 One of the teachers is selected at random. M is the event that the teacher selected is a male. A is the event that the teacher selected received an apple. B is the event that the teacher selected received a banana. C is the event that the teacher selected received an orange. (i) Find the following probabilities. (a) P( )MA , [2] (b) P( )MB . [2] (c) P( | )MC , [2] (ii) Determine whether the events M and C are independent, justifying your answer. [2] (ia) 1 4 2 103P( ) P( ) P( ) P( ) 2 15 25 150M A M A M A         Or 12 55 8 28 103P( ) 150 150MA     

(ib) 28 15 43P( ) 150 150MB    (ic) 8P( ) 8 150P( | ) 23P( ) 23 150 MCMC C    or n( ) 8P( | ) n( ) 23 MCMC C  (ii) 8P( | ) 23MC  but 1P( ) 2M   i.e. P( | ) P( )M C M  M and C not independent 2. In the year 2016, there were 620 male students and 520 female students in the JC1 cohort of Hwa Chong Institution (HCI). The number of these students studying H2 Mathematics, H2 Chemistry and H2 Physics are listed in the table below. One of the students is chosen at random. Events M, C and F are defined as follows: M : The student chosen is studying H2 Mathematics. C : The student chosen is studying H2 Chemistry. F : The student chosen is a female. Find (i)  'P MF , [1] (ii)  'P| MF , [2] (iii)  P CF [2] (iv) Give a reason in each case, state whether the following statements is True or False. (a) The events M and F are independent. [2] (b) The events M and C are not mutually exclusive. [1] 400 students were enrolled into HCI via the Joint Admission Exercise (JAE) in 2016. It was given that 25% of female students and 40% of male students who study H2 Mathematics were students who enrolled via the JAE. H2 Mathematics H2 Chemistry H2 Physics Male 610 480 306 Female 512 440 200 Total 1122 920 506

Three students who were enrolled via the JAE were chosen at random. (v) Find the probability all three of them are female students who study H2 Mathematics. [2] (vi) Find the probability that none of them study H2 Mathematics. [2] 2 (i) Total num