At one bank, it is known that 63% of customers have invested in a TFSA and 45% have invested in an RRSP. Also, if a customer has invested in an RRSP, there is a 75% chance they have also invested in a TFSA. Let T and R represent the events a customer has invested in a TFSA and an RRSP, respectively. In each part of this question, express each probability only in terms of the events T and R and justify any computation by explicitly stating the formula you are using. Do not define additional events. (a) Express each of the three probabilities listed above in terms of the events T and R. (b) Are the events T and R independent? Explain. (c) What is the probability a randomly selected customer has invested in (i) both a TFSA and an RRSP? (ii) a TFSA but not an RRSP? (iii) at least one of these two types of investment products?
At one bank, it is known that 63% of customers have invested in a TFSA and 45% have
invested in an RRSP. Also, if a customer has invested in an RRSP, there is a 75% chance they have also
invested in a TFSA. Let T and R represent the
respectively. In each part of this question, express each probability only in terms of the events T and R and
justify any computation by explicitly stating the formula you are using. Do not define additional events.
(a) Express each of the three probabilities listed above in terms of the events T and R.
(b) Are the events T and R independent? Explain.
(c) What is the probability a randomly selected customer has invested in
(i) both a TFSA and an RRSP?
(ii) a TFSA but not an RRSP?
(iii) at least one of these two types of investment products?
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