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You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a diamond each time.

User AndreKR
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1 Answer

6 votes
6 votes

Solution:

Given:

A 52-card deck

There are four suits in a standard deck of cards, Clubs, Hearts, Spades, and Diamonds.

There are 13 diamond cards.

Hence,


\begin{gathered} \text{Diamond cards = 13} \\ \text{Total cards = 52} \end{gathered}

Probability is calculated by;


\text{Probability}=\frac{n\text{ umber of required outcomes}}{n\text{ umber of total or possible outcomes}}

Thus, the probability of drawing a diamond on the first draw is;


\begin{gathered} \text{Probability of drawing a diamond}=\frac{n\text{ umber of diamond cards}}{\text{total number of cards}} \\ \text{Probability of drawing a diamond}=(13)/(52) \\ \text{Probability of drawing a diamond}=(1)/(4) \\ P(D_1)=(1)/(4) \end{gathered}

Since two draws are made with replacement, the cards are completed back again before the next draw.

Hence, the probability of drawing a diamond on the second draw is;


\begin{gathered} \text{Probability of drawing a diamond}=\frac{n\text{ umber of diamond cards}}{\text{total number of cards}} \\ \text{Probability of drawing a diamond}=(13)/(52) \\ \text{Probability of drawing a diamond}=(1)/(4) \\ P(D_2)=(1)/(4) \end{gathered}

Therefore, the probability of drawing a diamond each time;


\begin{gathered} P(D_1D_2)=(1)/(4)*(1)/(4) \\ P(D_1D_2)=(1)/(16) \end{gathered}

User Bowie Owens
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