Two cards are drawn at random. Find the probability that both the card

1.	Two cards are drawn at random. Find the probability that both the cards are of red colour or they are queen.
Answer» Let S = Sample – space. A = The event that the two cards drawn are red. B = The event that the two cards drawn are queen. A∩ B = The event that the two cards drawn are queen of red colour. \|S\|=C (52,2), \|A\| =C (26,2), \|B\| =C (4,2) n(A∩ B) =C (2,2) P(A) = \|A\| / \|S\|=C (26,2) /C (52.2) , P(B) = \|B\| / \|S\|=C (4,2) / C(52,2) P(A B) = \|A∩ B\| / \|S\|= C(2,2) /C (52,2) P(A⋃ B) = ? We have P(A⋃ B) = P(A) + P(B) – P(A∩ B) = C(26,2) /C (52.2)+C( 4,2) / C(52,2)–C (2,2) /C (52,2) = 55/221

Two cards are drawn at random. Find the probability that both the cards are of red colour or they are queen.

Answer»

Let S = Sample – space.

A = The event that the two cards drawn are red.

B = The event that the two cards drawn are queen.

A∩ B = The event that the two cards drawn are queen of red colour. |S|=C (52,2), |A| =C (26,2), |B| =C (4,2)

n(A∩ B) =C (2,2)

P(A) = |A| / |S|=C (26,2) /C (52.2) , P(B) = |B| / |S|=C (4,2) / C(52,2)

P(A B) = |A∩ B| / |S|= C(2,2) /C (52,2)

P(A⋃ B) = ?

We have P(A⋃ B) = P(A) + P(B) – P(A∩ B) = C(26,2) /C (52.2)+C( 4,2) / C(52,2)–C (2,2) /C (52,2) = 55/221

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Two cards are drawn at random. Find the probability that both the cards are of red colour or they are queen.

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