ACT 1 Alg: Find the probability of simple events

$Q_{1}:$ An ........... is one of the possible results that can occur as a result of a trial.

$Q_{2}:$ In the spinner modeled below, Sector $1$ has twice the area of Sector $3$. If the arrow is spun once, what is the probability that the arrow will land in Sector $1$?

$Q_{3}:$ Let $E$ be an event and $P(E )$ the probability it will occur. If $E$ is impossible, then $P(E)=$

$Q_{4}:$ Let $X$ be an event and $P(X )$ the probability it will occur. If it is certain that $X$ will occur (such as getting a prime number), $P(X) =$

$Q_{5}:$ The probability that event X will not occur is ?

$Q_{6}:$ An integer between $100$ and $999$, inclusive, is chosen at random. What is the probability that all three digits of the number are different odd numbers?

$Q_{7}:$ A bag contains $7$ blue marbles and $14$ marbles that are not blue. If one marble is drawn at random from the bag, what is the probability that the marble is blue?

$Q_{8}:$ If a fair coin is flipped three times, what is the probability that the result will be tails exactly twice?

$Q_{9}:$ If the probability that it will rain is $\frac{5}{12}$, then what is the probability that it will NOT rain?

$Q_{10}:$ If three coins are tossed, what is the probability that exactly two are heads?

$Q_{11}:$ Two dice are rolled. Find the probability that the sum of the two numbers is less than $4$?

$Q_{12}:$ The are $12$ pieces of colored chalk in a package $3$ white, $3$ yellow, $3$ orange, and $3$ green. If two pieces are selected at random, find the probability that both will be yellow?

$Q_{13}:$ The probability that Claire passes chemistry is $0.75$, and the probability that she passes history is $0.88$. If passing one course is independent of passing the other, what is the probability that she does not pass chemistry?

$Q_{14}:$ If the letters of the word $\textbf{PROBLEMS}$ are written on cards and put in a hat, what is the probability of randomly drawing either “E” or “S”?

$Q_{15}:$ Maya and Aya are going to get their driver’s licenses. The probability that Maya passes his driving test is $\frac{9}{10}$. The probability that Aya passes her driving test is $\frac{7}{9}$. Assuming that their result is not dependent on how the other does, what is the probability that Maya passes and Aya fails?

$Q_{16}:$ The probability of passing this week’s Language test is $70$ percent, and the probability of passing this week’s History test is $80$ percent. What is the probability of failing both tests?

$Q_{17}:$ A jar contains $4$ red, $1$ green, and $3$ yellow marbles. If $ 2$ marbles are drawn from the jar without replacement, what is the probability that both will be yellow?

$Q_{18}:$ ne marble is to be drawn randomly from a bag that contains three red marbles, two blue marbles, and one green marble. What is the probability of drawing a blue ?

$Q_{19}:$ If a gumball is randomly chosen from a bag that contains exactly $6$ yellow gumballs, $5$ green gumballs, and $4$ red gumballs, what is the probability that the gumball chosen is NOT green?

$Q_{20}:$ Noor has $4$ plaid shirts and $5$ solid-colored shirts hanging together in a closet. In his haste to get ready for work, he randomly grabs $1$ of these $9$ shirts. What is the probability that the shirt Noor grabs is plaid?

$Q_{21}:$ In a game, $80$ marbles numbered $00$ through $79$ are placed in a box. A player draws $1$ marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same ones digit (that is, both marbles have a number ending in $0, 1, 2, 3,$ etc.), the player is a winner. If the first marble drawn is numbered $35$, what is the probability that the player will be a winner on the next draw?

$Q_{22}:$ A partial deck of cards was found sitting out on a table. If the partial deck consists of $6$ spades, $3$ hearts, and $7$ diamonds, what is the probability of randomly selecting a red card from this partial deck? (Note: diamonds and hearts are considered “red,” while spades and clubs are considered “black.”)

$Q_{23}:$ Carol has an empty container and puts in $6$ red chips. She now wants to put in enough white chips so that the probability of drawing a red chip at random from the container is $\frac{3}{8}$. How many white chips should she put in?

$Q_{24}:$ An integer from $10$ through $99$, inclusive, is to be chosen at random. What is the probability that the number chosen will have $0$ as at least $1$ digit?

$Q_{25}:$ You are eating lunch at a restaurant and want to order a sandwich. There are twenty-five sandwiches on the menu, and six of them are toasted. If you order a sandwich at random, what is the probability of you ordering a sandwich that is not toasted?