Tobin's friend Rose claims that she can read minds. To test Rose's abilities, Tobin draws 3 cards without replacement from a standard deck of 52 playing cards. Tobin asks Rose to identify each of the 3 cards she drew in order.

Assume that Rose has no special abilities and is randomly guessing the cards.

What is the probability that Rose identifies all 3 cards in the correct order?

Choose 1 answer:
(A) $\frac{1}{{ }_{52} \mathrm{P}_{3}}$
(B) $\frac{1}{{ }_{52} \mathrm{C}_{3}}$
(C) $\frac{{ }_{3} \mathrm{C}_{1}}{{ }_{52} \mathrm{C}_{3}}$
(D) $\frac{\left({ }_{3} \mathrm{C}_{1}\right) \cdot\left({ }_{3} \mathrm{C}_{2}\right)}{{ }_{52} \mathrm{C}_{3}}$

Question

Tobin's friend Rose claims that she can read minds. To test Rose's abilities, Tobin draws 3 cards without replacement from a standard deck of 52 playing cards. Tobin asks Rose to identify each of the 3 cards she drew in order.

Assume that Rose has no special abilities and is randomly guessing the cards.

What is the probability that Rose identifies all 3 cards in the correct order?

Choose 1 answer:
(A) $\frac{1}{{ }_{52} \mathrm{P}_{3}}$
(B) $\frac{1}{{ }_{52} \mathrm{C}_{3}}$
(C) $\frac{{ }_{3} \mathrm{C}_{1}}{{ }_{52} \mathrm{C}_{3}}$
(D) $\frac{\left({ }_{3} \mathrm{C}_{1}\right) \cdot\left({ }_{3} \mathrm{C}_{2}\right)}{{ }_{52} \mathrm{C}_{3}}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the probability that Rose identifies all 3 cards in the correct order, we need to calculate the number of favorable outcomes over the total number of possible outcomes. ‖ ‖ step 2 ⋮ The number of ways to correctly guess the order of 3 cards drawn from a deck of 52 is 1, since there is only one correct order. ‖ ‖ step 3 ⋮ The total number of ways to draw 3 cards from a deck of 52 in a specific order is given by $52P3$, which is the number of permutations of 52 items taken 3 at a time. ‖ ‖ step 4 ⋮ Using the asksia-ll calculation list, we have $52P3 = (52!)/((52 - 3)!) = 132600$. ‖ ‖ step 5 ⋮ The probability that Rose guesses all 3 cards in the correct order is therefore $\frac{1}{52P3} = \frac{1}{132600}$. ‖ ∻1 Answer∻ ***A*** ∻Key Concept∻ ⚹Permutations and Probability⚹ ∻Explanation∻ ⚹The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event is guessing the correct order of 3 cards, which is a permutation problem.⚹◊What is the formula to calculate the permutation of choosing 3 cards without replacement from a deck of 52 playing cards?⍭ Generate me a similar question◊

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