Calculate the Theoretical probability of the following experiments. Use a tree diagram to visualize your calculations. *** Note that these
are independent experiments. Once she has removed a fruit, she
will put it back in before removing a second fruit.***
Jane has a bag with 5 oranges, 4 grapefruits, and 3 apples.
a) What is the probability that she will NO randomly take out two
oranges in a row?
b) What is the probability that she will NOT randomly take out two
grapefruits in a row?
c) What is the probability that she will NOI randomly take out two
apples in a row?
d) What is the probability that she will NOT take out an orange, then
an apple, and finally a grapefruit in that order?

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?