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49 votes
49 votes

A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?
 

  1. $\left(\dfrac{1}{5}\right)$  
  2. $\left(\dfrac{4}{25}\right)$  
  3. $\left(\dfrac{1}{4}\right)$  
  4. $\left(\dfrac{2}{5}\right)$
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7 Answers

Best answer
65 votes
65 votes

The number on the first card needs to be One higher than that on the second card, so possibilities are :

$\begin{array}{c}
\begin{array}{cc}
1^{\text{st}} \text{ card} & 2^{\text{nd}} \text{ card}\\
\hline
\color{red}1 & \color{red}-\\
2 & 1\\
3 & 2\\
4 & 3\\
5 & 4\\
\color{red}- & \color{red}5
\end{array}\\
\hline
\text{Total $:4$ possibilities}
\end{array}$

Total possible ways of picking up the cards $= 5 \times 4 = 20$

Thus, the required Probability $= \dfrac{\text{favorable ways}}{\text{total possible ways}}=  \dfrac{4}{20} = \dfrac 15$

Option A is correct

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25 votes
25 votes
Here we should consider without replacement, since "removed one at a time" means the card has been removed from the deck.

Prob of picking the first card  = 1/5

Now there are 4 cards in the deck. Prob of picking the second card = 1/4

Possible favourable combinations = 2-1, 3-2, 4-3, 5-4

Probability of each combination = (1/5)*(1/4) = 1/20

Hence answer = 4*1/20 = 1/5
7 votes
7 votes
the probability of choosing first no's is =(2,3,4,5)/(1,2,3,4,5)=4/5

the second time, we have only one option to choose out of four option=1/4

so,the total probability=(4/5)*(1/4)=1/5
5 votes
5 votes
with 5 cards to choose we can only fulfil the condition if we pick 2,3,4,5 in our choice else theres no way to get the same

so 4/(5*4) is the answer
Answer:

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