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,

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

The probability of picking card of less number is,

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

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

$P(6\text{ then less than 6\rparen=}\frac{1}{3}\times1=\frac{1}{3}$

Hence, the probability is 1/3.