Question

Cards are drawn one at a time without replacement from a deck of 52 ordinary playing cards.

(a) what is the probability that the 30th and the 40th cards are Kings?

(b) Given that the 30th card is a King, what is the conditional probability that the 40th card is also a King?
please solve it step by step​

Answer 1

Answer:-

Formula of Probability = Favourable outcomes/Total outcomes = FOC/TOC.

We have total of cards in a deck = 52.

The total number of kings in a deck = 4.

So, the Probability that any card is king = FOC/TOC = 4/52 = 2/26 = 1/13.

So, for the first question:-

• The probability that the 30th card of the Deck is a king = 1/13.
• The probability that 20th card of the Deck is a king = 1/13.

Now, it is given that 30th card is a king.

So, the probability that the 40th card is also king is:-

Total outcomes = 52 - 1 = 51.

Favourable outcomes = 4 - 1 = 3.

We reduce a number of king card from the favourable outcomes because it is given that one of the card is king for sure that is 30th card.

Similarly, we reduce the total number of cards because we are sure about one card to be king.

So, FOC/TOC = 3/51 = 1/17

• The probability for the 40th card to be also king:- 1/17.

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