Question

What is the possibility of choosing a red jack first and then choosing a red card without replacement

Answer 1

25/1326

Explanation:

In a standard deck of cards, there are 52 cards divided into 4 suits.

• Hearts (Red)

,

• Diamonds(Red)

,

• Spades(Black)

,

• Clubs (Black)

There are two red jacks and two black jacks.

Therefore:

`P(\text{ picking a red jack\rparen}=(2)/(52)`

Next, there are 26 red cards in a suit.

Since the selection is without replacement, the number of red cards has been reduced by 1. Therefore:

`P\text{ \lparen then choosing a red card\rparen}=(25)/(51)`

Multiply the two probabilities:

`\begin{gathered} P(\text{ choosing a red jack first and then a red card\rparen}=(2)/(52)*(25)/(51) \\ =(1)/(26)*(25)/(51) \\ =(25)/(1326) \end{gathered}`

The probability is 25/1326.

The third option is correct.