Mathematics, 29.07.2019 02:30 Jennifer16253

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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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 from: isabelvaldez123

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