4 cards are to be dealt successively and without replacement from an o

Question

4 cards are to be dealt successively and without replacement from an ordinary deck of 52 cards. What is the probability of receiving, in order, a spade, a heart, a diamond, and a club?

A. \frac{13}{52}⋅\frac{13}{51}⋅\frac{13}{50}⋅\frac{13}{49}

B. \frac{13}{52}⋅\frac{12}{51}⋅\frac{11}{50}⋅\frac{10}{49}

C. \frac{4}{52}⋅\frac{4}{51}⋅\frac{4}{50}⋅\frac{4}{49}

D. \frac{13}{52}⋅\frac{13}{52}⋅\frac{13}{52}⋅\frac{13}{52}

E. \frac{13}{52}⋅\frac{12}{52}⋅\frac{11}{52}⋅\frac{10}{52}

gmatophobia · Answer

In a pack of 52 cards, there are 13 cards of each type.

As we need the pick the cards in order, the first card, i.e. a spade, can be selected in 13 ways

Total number of cards = 52

Probability of selecting a spade =  \frac{13}{ 52}

Once a spade is select, we need to select a heart.

Number of hearts available = 13

Number of cards available = 51

Probability of selecting a spade =  \frac{13}{ 51}

We see that the number of cards in the denominator decreases by 1, while the number of cards in the numerator remains 13 (as a card of the same type was not selected previously).

Hence the same set of steps can be repeated for a diamond, and a club

Required probability =

\frac{13}{52}⋅\frac{13}{51}⋅\frac{13}{50}⋅\frac{13}{49}

Option A

Suvro1204 · Answer

Why we are decreasing the number in the denominator by as the question said without replacement? 
Thanks in advance

Posted from my mobile device

cat2010 · Answer

Suvro1204  ,Without replacement means we will not put that1 card back in the pack .

So, after picking first card and finding probability of spade ,we will discard this 1 particular card .

So for ,probability of heart ,total card will be = 52-1 = 51

If question was with replacemnt ,then we would have taken 52 in all cases .

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4 cards are to be dealt successively and without replacement from an o

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