Event A can be accomplished in 2 alternative ways, the cards drawn being

• 2 black
• 2 Queens

Alternative 1

	Black	Others	Total
Available	26	26	52
To Choose	2	0	2
Choices	26C2	26C0	52C0

Alternative 2

	Queen	Others	Total
Available	4	48	52
To Choose	2	0	2
Choices	4C2	48C0	52C0

Number of favorable choices

= Number of ways in which 2 cards can be drawn such that they are either both blacks or both queens

= Number of ways in which 2 blacks can be selected + Number of ways in which 2 queens can be selected

= (Number of ways in which 2 blacks can be selected from the available 26) + (Number of ways in which 2 queens can be selected from the available 4)

⇒ mA	=	mEA1 + mEA2
	=	26C2 + 4C2
	=	26 × 25 2 × 1 + 4 × 3 2 × 1
	=	(13 × 25) + (2 × 3)
	=	325 + 6
	=	331

Probability that either both are black of both are queen

⇒ 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
	=	331 1,326

Odds

Number of Unfavorable Choices

= Total Number of possible choices − Number of Favorable choices

⇒ mAc	=	n − mA
	=	1,326 − 331
	=	995

in favor

Odds in Favor of the cards drawn being both black or both queens

⇒ Odds in Favor of Event A

= Number of Favorable Choices : Number of Unfavorable Choices

= m_A : m_A^c

= 331 : 995

against

Odds against the cards drawn being both black or both queens

⇒ Odds against Event A

= Number of Unfavorable Choices : Number of Favorable Choices

= m_A^c : m_A

= 995 : 331

Odds (alternative)