When a certain type of thumbtack is​ flipped, the probability of its landing tip up​ (U) is 0.66 and the probability of its landing tip down​ (D) is 0.34. Suppose you flip two such​ thumbtacks, one at a time. Make a list of all the possible arrangements using U for up and D for down. Find the probabilities of each possible outcome.

Answer: There are 4 possibilities. They are all listed below with their percents.

You can create a tree diagram to shows all of the possibilities. It will start with 2 branches and then each of those branches will have 2 branches.

The possibilities are:  UU, UD, DU, DD

To find the probabilities of each, you have to multiply the percent for each together.

UU = 0.66 x 0.66 = 0.4356
UD = 0.66 x 0.34 = 0.2244
DU = 0.34 x 0.66 = 0.2244
DD = 0.34 x 0.34 = 0.1156