3. A lottery ticket can be purchased where the outcome is either a win or a loss. There is a 10% chance of winning the lottery (90% chance of losing) for each ticket. Assume each purchased ticket to be an independent event:

a) What is the probability of winning the lottery if 10 tickets are purchased? By winning, any one or more of the 10 tickets purchased result a win.

b) If you were to purchase lottery tickets in intervals of 10 (10, 20, 30, 40, 50, etc). How many tickets should you purchase to optimize you chance of winning. To answer this question, show a graph of probability of winning the lottery versus number of lottery tickets purchased.

Answer with Step-by-step explanation:

Since we have given that

Probability of winning the lottery = 10%

Probability of losing the lottery = 90%

a) What is the probability of winning the lottery if 10 tickets are purchased? By winning, any one or more of the 10 tickets purchased result a win.

Probability of winning atleast one of the 10 tickets is given  by

b) If you were to purchase lottery tickets in intervals of 10 (10, 20, 30, 40, 50, etc). How many tickets should you purchase to optimize you chance of winning. To answer this question, show a graph of probability of winning the lottery versus number of lottery tickets purchased.

n               P(n)

10             0.6513

20            0.8784

30            0.9576

40           0.9852

50           0.9948

60           0.9982

70           0.9993

80           0.9997

90           0.99992

100          0.99997

So, the probability of winning the lottery versus number of lottery tickets purchased is shown below:

i think it will be zero as slope has a formula of difference between initial and final distance divided by itz time interval

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: