A school club's daily new sign-ups $X$ take values $0,1,2,3$ with probabilities $0.18,0.27,k,0.31$. What is $k$?

The chart shows the probability distribution of $X$, the number of lunches one student buys in the cafeteria in a week. What is $P(X\ge 2)$?

A prize spinner has outcomes $0,1,2,3$ with probabilities $0.20,0.35,0.30,0.10$. What probability should replace $0.10$ to make a valid distribution?

The chart shows the probability distribution of $X$, the number of books returned to a library. What is $P(1\le X\le 3)$?

A bus stop's late buses $X=0,1,2,3,4$ have probabilities $0.16,0.22,0.38,k,0.09$. What is the missing probability $k$?

The chart shows the probability distribution of $X$, a student's quiz score gain. What is the probability that $X$ is not $1$?

The chart shows the probability distribution of $X$, the number of missed appointments at a clinic. What is $P(X>1)$?

The chart shows the probability distribution of $X$, the number of puppies a pet store has adopted. What is the probability that $X$ is at least $2$ but less than $5$?

A school raffle sells 500 tickets at $2 each. One ticket wins $300 and four tickets win $50 each. What is the expected value of one ticket to the buyer, counting the $2 price?

A carnival game costs $1.50 to play. The chart shows the probability distribution of the payout. What is the expected value per play?

A charity wheel costs $2 to spin. It pays $20 with probability $0.05$, $5 with probability $0.15$, and $0 otherwise. What is the expected value per spin?

A farm contest costs $1 to enter. A player wins $25 with probability $0.04$, $3 with probability $0.20$, and $0 otherwise. What is the expected value per entry?

A game costs $4. It pays $50 with probability $0.02$, $10 with probability $0.10$, and $0 otherwise. What is the expected value of one play?

A fundraiser sells 1000 tickets at $5 each. One ticket wins $1000 and five tickets win $100 each. What is the expected value of one ticket to the buyer?

A phone repair plan costs $12. A buyer receives a $100 repair with probability $0.08$ and $0 otherwise. What is the expected value to the buyer?

A booth game costs $2 to play. The chart shows the probability distribution of the payout. What is the expected value per play?

A teacher draws 5 students without replacement from a class of 20 in which 8 play an instrument, then counts instrument players. Which binomial condition does this fail?

A nurse screens donors until the first eligible donor is found and records the number screened. Eligibility probability is $0.30$ for each donor. Which binomial condition is missing?

A student rolls a fair die 12 times and counts how many rolls show a 6. Why is a binomial model appropriate?

A factory inspects 30 bulbs from a very large process where each bulb is defective with probability $0.04$ independently. Why is counting defective bulbs binomial?

A poll asks 25 freshmen and 25 seniors whether they drive to school; the yes probabilities are $0.20$ and $0.55$. Which binomial condition fails for the total yes count?

A coach records each of 20 athletes' best event as sprint, jump, or throw. Which binomial condition fails if the coach counts recorded event types?

A basketball player makes $70\%$ of free throws independently. What is the probability she makes exactly 4 of her next 5 free throws, to three decimals?

A seed germinates with probability $0.80$ independently. What is the probability exactly 5 of 6 planted seeds germinate, to three decimals?

A medical screen has false positives with probability $0.10$ independently. What is the probability exactly 2 of 8 healthy patients get false positives, to three decimals?

A soccer player scores on a penalty kick with probability $0.60$ independently. What is the probability of scoring on at least 3 of 4 kicks, to three decimals?

A shipment item is defective with probability $0.03$ independently. What is the probability that none of 20 inspected items are defective, to three decimals?

An email gets a response with probability $0.25$ independently. What is the probability exactly 3 of 10 emails get responses, to three decimals?

A package arrives on time with probability $0.90$ independently. What is the probability exactly 10 of 12 packages arrive on time, to three decimals?

A blood donor has type O with probability $0.40$ independently. What is the probability that at most 2 of 7 donors have type O, to three decimals?

A machine fills 400 bottles, and each bottle is underfilled with probability $0.05$ independently. What are the mean and standard deviation of the underfilled count?

A flight is late with probability $0.12$ independently. For 50 flights, what are the mean and standard deviation of the number that are late?

A player makes a free throw with probability $0.75$ independently. For 80 shots, what are the mean and standard deviation of the made-shot count?

A chip is faulty with probability $0.02$ independently. For 200 chips, what are the mean and standard deviation of the faulty-chip count?

A voter supports a proposal with probability $0.55$ independently. For 120 voters, what are the mean and standard deviation of the support count?

A caller's phone call is answered with probability $0.25$ independently. What is the probability the first answered call is the fourth call, to three decimals?

A seed sprouts with probability $0.30$ independently. What is the probability the first sprouting seed is the third seed checked, to three decimals?

A printer jams on a day with probability $0.08$ independently. What is the probability the first jam happens on the fifth day, to three decimals?

A basketball player makes a shot with probability $0.65$ independently. What is the probability the first made shot is the second shot, to three decimals?

An inspected part is faulty with probability $0.15$ independently. What is the probability the first faulty part is the seventh part inspected, to three decimals?