In a group of 50 students, 40 study Mathematics, 32 study Physics, and each student studies at least one of these subjects. a. Use a Venn diagram to find how many students study both subjects. b. If a student from this group is randomly selected, find the probability that he or she: i. studies Mathematics but not Physics ii. studies Physics given that he or she studies Mathematics.

In a year group of 63 students, 22 study Biology, 26 study Chemistry and 25 study Physics. 18 study both Physics and Chemistry, four study both Biology and Chemistry and three study both Physics and Biology. One studies all three subjects. How many students study: a. Biology only b. Physics or Chemistry c. none of Biology, Physics or Chemistry d. Physics but not Chemistry?

Three bags contain different numbers of blue and red marbles. Bag A has 3 Red and 2 Blue marbles, Bag B has 4 Red and 1 Blue marbles, and Bag C has 2 Red and 3 Blue marbles. A bag is selected using a die which has three A faces, two B faces, and one C face. One marble is then selected randomly from the bag. Determine the probability that the marble is: red.

In a group of 40 students, 22 study Economics, 25 study Law, and 3 study neither of these subjects. Determine the probability that a randomly chosen student studies: at least one of these subjects

Three bags contain different numbers of blue and red marbles. Bag A has 3 Red and 2 Blue marbles, Bag B has 4 Red and 1 Blue marbles, and Bag C has 2 Red and 3 Blue marbles. A bag is selected using a die which has three A faces, two B faces, and one C face. One marble is then selected randomly from the bag. Determine the probability that the marble is: blue

Biologists doing studies in a particular environment often tag and release subjects in order to estimate the size of a population or the prevalence of certain features in the population. Ten animals of a certain population thought to be extinct (or near extinction) are caught, tagged, and released in a certain region. After a period of time, a random sample of 15 of this type of animal is selected in the region. What is the probability that 5 of those selected are tagged if there are 25 animals of this type in the region?