A player chooses one card from Deck A and one card from Deck B. What is the probability that the player will choose a C2 card from the first deck or a C6 card from the second deck?

The probability of choosing a C3 card from Deck A or choosing a C5 card from Deck B is

(Use a simplified fraction to represent the probability).

The probability that the player will choose a C2 card from the first deck or a C6 card from the second deck is 17/42
The probability that the player will choose a C3 card from the first deck or a C5 card from the second deck is 9/14

There are 4 C2 cards in the first deck out of a total of 12 cards, and there are 3 C6 cards in the second deck out of a total of 14 cards.

So, the probability that the player will choose a C2 card from the first deck or a C6 card from the second deck is:

[tex]P = \frac{4}{12} + \frac{3}{14}[/tex]

Simplify

[tex]P = \frac{1}{3} + \frac{3}{14}[/tex]

Take the LCM

[tex]P = \frac{14 + 3}{42}[/tex]

[tex]P = \frac{17}{42}[/tex]

Also;

There are 3 C3 cards in the first deck out of a total of 12 cards, and there are 4 C5 cards in the second deck out of a total of 14 cards.

So, the probability that the player will choose a C3 card from the first deck or a C5 card from the second deck is:

[tex]P = \frac{3}{12} + \frac{4}{14}[/tex]

Simplify

[tex]P = \frac{1}{4} + \frac{2}{7}[/tex]

Take the LCM

[tex]P = \frac{4 + 14}{28}[/tex]

[tex]P = \frac{18}{28}[/tex]

[tex]P = \frac{9}{14}[/tex]

Hence, the probability that the player will choose a C3 card from the first deck or a C5 card from the second deck is 9/14