What is the probability of spinning a 2 on the spinner shown below?

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