Question 1: In the population of males the following statistics are recorded:

• There is a 64.1% chance a randomly selected male has brown hair,
• There is a 4.3% chance a randomly selected male has red hair,
• There is 14.5% chance a randomly selected male has blue eyes,
• There is 19.3% chance a randomly selected male has hazel eyes,
• There is a 8.5% chance a randomly selected male has brown hair and blue eyes
• There is a 21.1% chance a randomly selected male has either red hair or hazel eyes (or both)

(a)What is the probability that a randomly selected male has either brown hair or blue eyes (or both)?(2 marks)

• 0.632
• 0.056
• 0.701
• 0.483
• 0.912

(b)What is the probability that a randomly selected male has red hairand hazel eyes?(2 marks)

• 0.025
• 0.036
• 0.921
• 0.182
• 0.285

(c)What is the probability that a randomly selected male has blue eyes given that they have brown hair?(2 marks)

• 0.167
• 0.372
• 0.209
• 0.654
• 0.133

(d)What is the probability that a randomly selected male has hazel eyes given that they have red hair?(2 marks)

• 0.581
• 0.376
• 0.023
• 0.298
• 0.981

(e)What is the probability that a randomly selected male has brown hair anddoes nothave blue eyes?(2 marks)

• 0.390
• 0.556
• 0.212
• 0.189
• 0.623

(f)What is the probability that a randomly selected male doesnot havered hair andhas hazel eyes?(2 marks)

• 0.012
• 0.897
• 0.934
• 0.198
• 0.168

(g)What is the probability that a randomly selected male has brown hair given that theydo nothaveblue eyes?(2 marks)

• 0.907
• 0.321
• 0.289
• 0.650
• 0.778

Question 2: There is a 5% chance that a randomly selected individual will have O-negative blood.Suppose we randomly select 15 individuals from the population and test them for O-negative blood. LetXdenote the number of individuals in the sample that have O-negative blood.

(a)What is the distribution ofXin conventional statistical notation?(2 marks)

• B(15, 0.05)
• B(15, 0.95)
• B(15, 7125)
• B(0.05, 15)
• N(15, 0.005)

(b)What is the probability that at least 2 individuals in the sample have O-negative blood?(2 marks)

• 0.9638
• 0.1710
• 0.0362
• 0.8290
• 0.0934

(c)What is the probability that less than 5 individuals in the sample have O-negative blood?(2 marks)

• 0.9999
• 0.3812
• 0.4633
• 0.9994
• 0.0006

(d)What is the P(1 < X4) equal to?(2 marks)

• 0.0356
• 0.5361
• 0.3896
• 0.1704
• 0.0678

(e)How many adults in the sample do we expect to have O-negative blood?(2 marks)

• 1
• 0.75
• 5
• 15
• 3

(f)What is the variance ofX?(2 marks)

• 1.9267
• 2
• 0.8441
• 15
• 0.7125