Typically, zero or one workplace health and safety incidents occur every month at an aluminium refinery. In any given month, whether or not a health and safety incident occurs, and the seriousness of the incident if it does occur, is expected to agree with the following table: n No incident Minor incident Major incident Pr(N = n) 0.29 0.31 0.40 In this table, n is a descriptive value which describes two things: (1) whether or not a health and safety incident occurs and (2) the seriousness of the incident if it does occur. a) Explain whether or not the table is a valid probability mass function. (Note that, according the Lecture Notes, a discrete variable can be numerical or descriptive.) (1 mark) b) Because the table above is quite alarming, all staff have recently undergone health and safety training. The aluminium refinery's Health and Safety Officer will consider this training a success if, over the next 50 months, there are 12 months or less out of 50 months in which there are major health and safety incidents. Based on the table above, use the binomial distribution to estimate the probability of observing this "success" if no training occurred. (2 marks)