Question

When a certain b pe of thumblack isRipped, the probability of it landing tip up (U) is 0,71 and Ina probablity of its landing tip down (D) is 0.29. Buppose youtime. Make a list of all the possible arrangements using U for up and D for down, Find the probabilities of each possible outcom

Answer 1

Step-by-step explanation

From the statement, we know that the probabilities of the events U and D are:

• P(U) = 0.71,

,

• P(D) = 0.29.

If we flip the thumbtack two times, we have four possible results:

0. UU,

,

1. UD,

,

2. DU

,

3. DD.

Because the result of each flip is independent of the other, the probability of each arrangement is the product of the probability of each event:

`\begin{gathered} P(UU)=P(U)*P(U)=0.71*0.71=0.5041, \\ P(UD)=P(U)*P(D)=0.71*0.29=0.2059, \\ P(DU)=P(D)*P(U)=0.29*0.71=0.2059, \\ P(DD)=P(D)*P(D)=0.29*0.29=0.0841. \end{gathered}`

Answer

D. There are four arrangements: UU, UD, DU, and DD. The probabilities are:

• P(UU) =, 0.5041

,

• P(UD) = ,0.2059

,

• P(DU) =, 0.2059

,

• P(DD) =, 0.0841