Let X be the random variable that represents the number of consecutive days in which the parking lot is occupied before it is unoccupied. Then the variable X is a geometric random variable with probability of success p = 2/3, with probability function f (x) = [(2/3)^x] (1/3)
Then the probability of finding him unoccupied after the nine days he has been found unoccupied is:
P (X> = 10 | X> = 9) = P (X> = 10) / P (X> = 9). For a geometric aeatory variable:
P (X> = 10) = 1 - P (X <10) = 0.00002
P (X> = 9) = 1 - P (X <9) = 0.00005
Thus, P (X> = 10 | X> = 9) = P (X> = 10) / P (X> = 9) = 0.00002 / 0.00005 = 0.4.
The sequence is " Algebraic, common difference = −10 " ⇒ 1st answer
Step-by-step explanation:
Let us revise the algebraic and geometric sequences
The Algebraic sequence is the sequence that has a common difference between each two consecutive terms, like 2 , 5 , 8 , 11 , 14 , .......... the difference between the 5 and 2 is equal to the difference between 8 and 5, and the difference between 11 and 8 and the difference between 14 and 11
The geometric sequences is the sequence that has a common ratio between each two consecutive terms, like 3 , -9 , 27 , -81 , ...... the ratio between -9 and 3 as the ratio between 27 and -9 as the ratio between -81 and 27
→ x : 1 : 2 : 3 : 4
→ f(x) : 5 : -5 : -15 : -25
x represents the positions of the terms
f(x) represents the value of each term
∵ 1st = 5 and 2nd = -5
∵ -5 - 5 = -10
∵ 2nd = -5 and 3rd = -15
∵ -15 - (-5) = -15 + 5 = -10
∵ 3rd = -15 and 4th = -25
∵ -25 - (-15) = -25 + 15 = -10
∴ There is a common difference -10 between each two
consecutive terms
∴ The sequence is algebraic with common difference -10
The sequence is " Algebraic, common difference = −10 "
