Event A can be accomplished in 4 alternative ways, the cards drawn being

• 2 spades
• 2 clubs
• 2 hears
• 2 diamonds

Alternative 1

	Spades	Others	Total
Available	13	39	52
To Choose	2	0	2
Choices	13C2	39C0	52C0

Alternative 2

	Clubs	Others	Total
Available	13	39	52
To Choose	2	0	2
Choices	13C2	39C0	52C0

Alternative 3

	Hearts	Others	Total
Available	13	39	52
To Choose	2	0	2
Choices	13C2	39C0	52C0

Alternative 4

	Diamonds	Others	Total
Available	13	39	52
To Choose	2	0	2
Choices	13C2	39C0	52C0

Number of favorable choices

= Number of ways in which 2 cards are drawn such that they belong to the same suite

= Number of ways in which 2 spades can be selected + Number of ways in which 2 clubs can be selected + Number of ways in which 2 hearts can be selected + Number of ways in which 2 diamonds can be selected

= (Number of ways in which 2 spades can be selected from the available 13) + (Number of ways in which 2 clubs can be selected from the available 13) + (Number of ways in which 2 hearts can be selected from the available 13) + (Number of ways in which 2 diamonds can be selected from the available 13)

⇒ mA	=	mEA1 + mEA2 + mEA3 + mEA4
	=	13C2 + 13C2 + 13C2 + 13C2
	=	13 × 12 2 × 1 + 13 × 12 2 × 1 + 13 × 12 2 × 1 + 13 × 12 2 × 1
	=	(13 × 6) + (13 × 6) + (13 × 6) + (13 × 6)
	=	78 + 78 + 78 + 78
	=	312

Probability of the cards drawn belonging to the same suit

⇒ Probability of occurrence of Event A

=	Number of Favorable Choices for the Event Total Number of Possible Choices for the Experiment

⇒ P(A)	=	mA n
	=	312 1,326
	=	4 17

Odds

Number of Unfavorable Choices

= Total Number of possible choices − Number of Favorable choices

⇒ mAc	=	n − mA
	=	1,326 − 312
	=	1,014

in favor

Odds in Favor of the cards drawn belonging to the same suit

⇒ Odds in Favor of Event A

= Number of Favorable Choices : Number of Unfavorable Choices

= m_A : m_A^c

= 312 : 1,014

= 4 : 13

against

Odds against the cards drawn belonging to the same suit

⇒ Odds against Event A

= Number of Unfavorable Choices : Number of Favorable Choices

= m_A^c : m_A

= 1,014 : 312

= 13 : 4

Odds (alternative)