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

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}

Explanation:

The probability that it lands tip up is 20% P(U) =
`(20)/(100) = (1)/(5)`

The probability that it lands tip up is 80% P(D) =
`(80)/(100) =(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} =
  `(1)/(5) X (1)/(5) = (1)/(25)`

• Probability of getting two lands tip down= P{ DD} =
  `(4)/(5) X (4)/(5) = (16)/(25)`

• Probability of getting one tips up and one tips down P{UD} =
  `(1)/(5) X (4)/(5) = (4)/(25)`

• Probability of getting one tips down and one tips up P{DU} =
  `(4)/(5) X (1)/(5) = (4)/(25)`

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

that is =
`(1)/(25) +(16)/(25) +(4)/(25)+(4)/(25) =(25)/(25) =1`