Question

You pick a card at random. Without putting the first card back, you pick a second card at random.What is the probability of picking a 6 and then picking a number less than 6?Simplify your answer and write it as a fraction or whole number.

Answer 1

Given,

The number of cards are 6, 5, and 4.

Required

The probability of picking card 6 then card less than 6 from the remaining.

The probability of picking card 6 is,

`\begin{gathered} P(6)=\frac{number\text{ of card 6}}{total\text{ number of cards}} \\ =(1)/(3) \end{gathered}`

The probability of picking card of less number is,

`\begin{gathered} P(5\text{ or 4})=\frac{number\text{ of card 5 or 4}}{total\text{ number of cards}} \\ =(2)/(3-1) \\ =1 \end{gathered}`

The probability of picking card 6 then card less than 6 from the remaining.

`P(6\text{ then less than 6\rparen=}(1)/(3)*1=(1)/(3)`

Hence, the probability is 1/3.