Question

Helen has 20 knit hats to sell. She has 5 green hats, 8 blue hats, and 7 orange hats. She will choose a hat and record its color. Without replacing the hat. she will randomly choose a second hat and record its color. What is the probability of choosing two blue hats in a row?

Answer 1

Let's begin by listing out the information given to us:

Total number of hats = 20

Number of green hats = 5

Number of blue hats = 8

Number of orange hats = 7

The probability of choosing 2 blue hats in a row without replacement is calculated as shown below:

`\begin{gathered} For\text{ the first choosing, we have:} \\ P(blue)=\frac{No\mathrm{}Of\mathrm{}BlueHats}{TotalHats}=(8)/(20)=(2)/(5) \\ P(blue)=(2)/(5) \\ \\ \text{For the second choosing, we have:} \\ P(blue)=(NoOfBlueHats(Left))/(TotalHats(Left))=(7)/(19) \\ P(blue)=(7)/(19) \\ \\ The\text{ probability of choosing two blue hats in a row is:} \\ P(TwoBlueHatInARow)=(2)/(5)*(7)/(19)=(14)/(95) \\ P(TwoBlueHatInARow)=(14)/(95) \end{gathered}`