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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.

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MrEquation
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

Answer:

The total number of possible ways are: {(U,U), (U,D), (D,U), (D,D)}

The required table is shown below:

                          UU          UD           DU        DD

Probability     0.4356   0.2244   0.2244   0.1156

Step-by-step explanation:

Consider the provided information.

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.

Part (A) We need to make a list of all the possible arrangements using U for up and D for down.

Let both thumbtack landing tip up​ (U) = (U,U)

Let one thumbtack landing tip up​ and landing tip of second is down = (U,D), (D,U)

Let both thumbtack landing tip down (D) = (D,D)

Hence, the total number of possible ways are: {(U,U), (U,D), (D,U), (D,D)}

Thus, there are 4 possible ways.

Part (B) Find the probabilities of each possible outcome.

It is given that landing tip up​ (U) is 0.66 and the probability of its landing tip down​ (D) is 0.34.

Probability of (U,U) is = 0.66×0.66=0.4356

Probability of (U,D) is = 0.66×0.34=0.2244

Probability of (D,U) is = 0.34×0.66=0.2244

Probability of (D,D) is = 0.34×0.34=0.1156

The required table is shown below:

                          UU          UD           DU        DD

Probability     0.4356   0.2244   0.2244   0.1156

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