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?
why total possiblity is , 20 not 25 ?
If anyone is confused about how sample space is 20 and not 25. The reason is question is considering “without replacement”. Hence there are 5 ways to choose 1st card and 4 ways to choose the 2nd card ,hence the |SS|=5x4=20
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
The point which i missed :- they are asking only 1 higher
“Two cards are then removed one at a time from the deck”
i think due to this line it’s w/o replacement
M I right? @Umair alvi
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