Topic
Q:
PROBLEM
Simon must answer two security questions in order to reset his forgotten password to his AOL account from 1996. The
probability he remembers the answer to the first security question is .6 . The probability that he fails to remember the
answer to the second question is .6. What is the probability that Simon successfully answers both questions correctly?
Q:
A college foundation raises funds by selling 600 raffle tickets for a new car worth \( \$ 46,000 \) at \( \$ 140 \) each.
(a) Find the expected net winnings of a person buying one of the tickets.
(b) Find the total profit for the foundation, assuming they had to purchase the car.
(c) Find the total profit for the foundation, assuming the car was donated.
(a) The expected net winnings are \( \$ \)
(Round to the nearest hundredth as needed.)
Q:
Let
\[ f(x)=\left\{\begin{array}{ll}0.048 x(5-x) & 0 \leq x \leq 5 \\ 0 & \text { otherwise }\end{array}\right. \]
(a) Verify that \( f \) is a probability density function.
(b) Find \( P(X \geq 4) \).
Q:
The expected value of betting \( \$ 1 \) on one roulette number is
approximately \( -\$ .05 \). What does this mean in practical terms?
If many people made this bet over the course of the night, the
house would expect to take in approximately a \( 5 \% \) return.
If I bet \( \$ 1 \) one time, I would expect to leave the table with
approximately 95 cents.
I am almost guaranteed to lose this bet
I am almost guaranteed to win this bet
Q:
1. Let \( X \) be a continuous random variable whose probability density function is
\[ f(x)=\left\{\begin{array}{ll}\frac{x^{3}}{4} & 0 \leq x \leq c \\ 0 & \text { otherwise }\end{array}\right. \]
What is the value of \( c \) that makes \( f(x) \) a valid probability density function (PDF).
Q:
A person uses his car \( 30 \% \) of the time, walks \( 30 \% \) of the time
and rides the bus \( 40 \% \) of the time as he goes to work. He is late
\( 10 \% \) of the time when he walks; he is late \( 3 \% \) of the time when
he drives; and he is late \( 7 \% \) of the time he takes the bus. What
is the probability he took the bus if he is late? (round to 3
decimal places)
Q:
You run an ice cream shop. You notice that the following
probabilities of orders:
\( \mathrm{P}( \) Vanilla \( )=.3 \)
\( \mathrm{P}( \) Sundae \( )=.2 \)
\( \mathrm{P}( \) Vanilla \& Sundae \( )=.15 \)
You want to find the satisfaction rating of customers who
ordered Sundaes. If you were to randomly select one customer
who ordered a Sundae for their feedback, what is the
probability that they purchased a Vanilla Sundae?
Q:
ACTIVIDADES DE REFORZAMIENTO.
Ejercicio 1. Los dispositivos electrónicos generalmente requieren de un código personal para
funcionar, Manuel compró un celular que requiere de un código de 4 digitos y solo puede
escoger para hacer su contraseña de un conjunto de 10 digitos que son: \( 0,1,2,3,4,5,6,7 \),
8, 9. ¿Cuántos códigos se pueden hacer si cualquier digito que participó en una permutación
puede tomarse nuevamente?
Q:
Las preguntas 9 y 10 se responden de acuerdo con la siguiente información: Un grupo de
amigos está formado por 4 hombres y 4 mujeres.
9. ¿De cuántas maneras diferentes se podrían sentar en una fila de 8 puestos si los del
mismo sexo deben auedar siembre iuntos?
Q:
38. In a non leap year, the probability of
getting 53 sundays or 53 Tuesdays or 53
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