Q. 335.0( 1 Vote )

A card is d

Answer :

Given that two cards are drawn from the deck with replacement.

We know that there will four suits in a deck and each suit contains 13 cards namely Spades, Hearts, Diamonds, Clubs.

Also, there will total of 4 aces and 2 red queens and 2 black queens

Let us find the probability required:

P(Dsame) = P(For selecting a card from a single suit out of 52 cards)

This probability will be same for all the suits.

P(Dace) = P(Drawing an ace)

P(DredQ) = P(Drawing a red queen)

We need to find the probability of getting:

i. Both cards from same deck

ii. First an ace and second a red queen

P(Ssame) = P(getting both cards from same deck)

We may get two cards any of the four decks. So, each deck’s probability is taken into consideration.

P(Ssame) = P(both cards from spade) + P(both cards from hearts) + P(both cards from diamond) + P(both cards from club)

Since drawing a card is an independent event, their probabilities multiply each other.

P(Ssame) = (P(DS)P(DS)) + (P(DH)P(DH)) + (P(DD)P(DD)) + (P(DC)P(DC))

P(SAR) = P(getting an ace first and followed red queen)

Since drawing a card is an independent event, their probabilities multiply each other.

P(SAR) = (P(DA)P(DredQ))

The required probabilities are .

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