(a) The probability that an automobile being filled with gasoline will also need an oil change is 0.35; the probability that it needs a new oil filter is 0.45; and the probability that both the oil and filter need changing is 0.25. (i) If the oil had to be changed, what is the probability that a new oil filter is needed ? (ii) If a new oil filter is needed, what is the probability that the oil has to be changed ? (b) 3 Cards are drawn in succession without replacement from an ordinary deck. Find the probability of the event A1 ∩ A2 ∩ A3, where A1 is the event that the first card is RED ace, A2 is the event that the second card Queen or King and A3 is the event that the third card which is greater than 3 and less than Eight ?
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.
(a) The probability that an automobile being filled with gasoline will also need an oil change is 0.35; the probability that it needs a new oil filter is 0.45; and the probability that both the oil and filter need changing is 0.25.
(i) If the oil had to be changed, what is the probability that a new oil filter is needed ?
(ii) If a new oil filter is needed, what is the probability that the oil has to be changed ?
(b) 3 Cards are drawn in succession without replacement from an ordinary deck. Find the probability of the
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