1.2) Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 22 of the 51 boxes on the shelf have the secret decoder ring. The other 29 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring? (Give answer as a decimal correct to four decimal places.) _____________

2.3) When doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial samples of different blood specimens. If samples from five people are combined and the mixture tests negative, we know that all five individual samples are negative. Find the probability of a positive result for five samples combined into one mixture, assuming the probability of an individual blood sample testing positive for the virus is 0.1. Round the answer to four decimal place accuracy. ______________

3.4) In a large population, 52 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal to at 4 places. _____________

4.5) Round all answers to 4 decimal places.

a. A bag contains 5 red marbles, 8 black marbles, and9 white marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a red marble and then a white marble? ________________

b. A bag contains 8 blue marbles, 9 white marbles, and5 black marbles.If two different marbles aredrawn from the bag , what is the probability of drawing first a blue marble and then a black marble? ________

5.6) Use the following probabilities to answer the question. Round to 4 decimal places. P(A)=0.72, P(B)=0.18 P(A and B)=0.10 P(BA)= ___________

6.7) A jar contains 8 red marbles numbered 1 to 8 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability of the given event, please show your answers as reduced fractions. (a) The marble is red. P(red)= (b) The marble is odd-numbered. P(odd)= (c) The marble is red or odd-numbered. P(red or odd) = (d) The marble is blue or even-numbered. P(blue or even) =

7.8) A survey of athletes at a high school is conducted, and the following facts are discovered: 27% of the athletes are football players, 48% are basketball players, and 14% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player? ________________ % (Please enter your answer as a percent)