Question

1. What approach has been used to derive the following probability numbers? (10)

We have discussed three approaches to arrive at probability numbers. Parts a-c test your understanding of these approaches.

1. Out of the last 400 days in Portland, it rained 40 days. Hence, the probability of rain in any given day is 0.1. The approach used to derive at probability is __________________________________.
2. The probability of drawing a spade in a deck of 52 cards is 0.25. The approach used to derive at probability is __________________________________.
3. An experienced doctor tells when seeing a terminally ill cancer patient that the chances of this patient’s survival are 5%. The approach used to derive at probability is __________________________________.

Calculate answers to the following questions. Show your work.

4. The odds for an event with probability of 0.41 are _____________.
5. The odds for an event are 5 to 11. In terms of a probability number, this value is _____.

Answer 1

a) The approach here to define probability = Total outcomes of the event occuring/Total outcomes = 40/400 = 0.1

b) There are total 13 spades in a standard deck of 52 cards. So the probability of drawing a spade = 13/52 = 0.25 (So the approach is same as above, total outcomes of the event/Total number of outcomes)

c) Here the doctor bases the probability of survival on the whole experience of survival in the population so far. So he uses past experience of survival of such cases and tells the patient the same percentage.

d) Odds of an event = Probability that the event will occur/Probability that the event will not occur = 0.41/(1-0.41) = 0.6949

d) Odds = 5/11

Let probability that event will occur be p

So the probability that the event will not occur = 1-p

So, p/1-p = 5/11

Or, 11p = 5 - 5p

Or, 16p = 5

Or, p= 5/16 = 0.3125