The price at which the crude oil extracted from Alberta’s tar sands can be sold is determined by the “Brent Crude” price at which crude oil is traded. At a Brent Crude price of $60/barrel 42% of the oil in the tar sands can be extracted profitably. (a) A market research company forecasts the Brent Crude price will be over $60/barrel next year with a probability of 0.9 and that it will be over $60/barrel the following year with a probability of 0.8. These two forecasts are independent of each other. (i) What is the probability that the Brent Crude price will be over $60/barrel both next year and also the following year? (ii) What is the probability that the Brent Crude price will be over $60/barrel either next year or the following year or both years? (b) Ignore the forecast in part (a). A market research company forecasts the Brent Crude price will be over $60/barrel next year with a probability of 0.8. The forecast for the following year depends on whether the price next year is in fact over $60/barrel. If it is, then the probability of being over $60/barrel the following year is 0.7. If the actual Brent Crude price is not over $60/barrel next year then the probability of being over $60/barrel the following year is 0.4. (i) What is the probability that the Brent Crude price will be over $60/barrel next year and under $60/barrel the following year. (ii) What is the probability that the Brent Crude price will be over $60/barrel in exactly one of the next two years?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The price at which the crude oil extracted from Alberta’s tar sands can be sold is determined by the “Brent Crude” price at which crude oil is traded. At a Brent Crude price of $60/barrel 42% of the oil in the tar sands can be extracted profitably.
(a) A market research company forecasts the Brent Crude price will be over $60/barrel next year with a
(i) What is the probability that the Brent Crude price will be over $60/barrel both next year and also the following year?
(ii) What is the probability that the Brent Crude price will be over $60/barrel either next year or the following year or both years?
(b) Ignore the forecast in part (a). A market research company forecasts the Brent Crude price will be over $60/barrel next year with a probability of 0.8. The forecast for the following year depends on whether the price next year is in fact over $60/barrel. If it is, then the probability of being over $60/barrel the following year is 0.7. If the actual Brent Crude price is not over $60/barrel next year then the probability of being over $60/barrel the following year is 0.4.
(i) What is the probability that the Brent Crude price will be over $60/barrel next year and under $60/barrel the following year.
(ii) What is the probability that the Brent Crude price will be over $60/barrel in exactly one of the next two years?
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