Question

When a certain type of thumbtack is tossed, the probability that it lands tip up is 20%, and the probability that it lands tip is 80%. All possible outcomes when two thumbtacks are tossed are listed. U means the tip is up and D means the tip is down.

Answer 1

Answer:

All possible outcomes when two thumbtacks are tossed are listed

{ UU ,UD,DU,DD} here U means the tip is up and D means the tip is down.

The probabilities of all these possible outcomes are

{ p(UU) ,p(UD),p(DU),p(DD)} are {1/25 , 4/25 ,4/25 , 16/25}

Step-by-step explanation:

The probability that it lands tip up is 20% P(U) =  $\frac{20}{100} = \frac{1}{5}$

The probability that it lands tip up is 80% P(D) =  $\frac{80}{100} =\frac{4}{5}$

All possible outcomes when two thumbtacks are tossed are listed

{ UU ,UD,DU,DD} here U means the tip is up and D means the tip is down.

• Probability of getting two lands tip up = P{ UU} = $\frac{1}{5} X \frac{1}{5} = \frac{1}{25}$  

• Probability of getting two lands tip down= P{ DD} = $\frac{4}{5} X \frac{4}{5} = \frac{16}{25}$

• Probability of getting one tips up and one tips down   P{UD} =$\frac{1}{5} X \frac{4}{5} = \frac{4}{25}$      

•  Probability of getting one tips down and one tips up   P{DU} =$\frac{4}{5} X \frac{1}{5} = \frac{4}{25}$    

note:- The sum of all probabilities is equal to one

that is = $\frac{1}{25} +\frac{16}{25} +\frac{4}{25}+\frac{4}{25} =\frac{25}{25} =1$