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.

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

300pi

step-by-step explanation: