Question

Declan's friend Luka claims that he can read minds. To test Luka's abilities, Declan draws 5 cards without replacement from a standard deck of 52 playing cards. Declan then asks Luka to identify in any order which 5 cards he drew without looking. Assume that Luka has no special abilities and is randomly guessing the cards. What is the probability that Luka correctly identifies all 5 cards in any order? :

Answer 1

Answer:

1/52c5 (b)

​

Step-by-step explanation:

Answer 2

The probability Luka correctly identifies all 5 cards in any order is  $\frac{1}{^{52}C_{5}}$.

What is probability?

"Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen."

We have

The number of favorable outcomes are Luka correctly identifying all 5

5 cards in any order, and this can be done in $^{5}C_{5}$  ways. This is equal to 1.

∴ The number of favorable outcomes are 1

Luke can identify 5 cards from 52 cards in  $^{52}C_{5}$  ways (because there is no order followed here).

∴ The total number of outcomes are $^{52}C_{5}$

Formula for probability of an event happening

=  $\frac{Number of Favorable Outcomes}{Total Number of Favorable Outcomes}$

​So the probability Luka correctly identifies all 5 cards in any order is

= $\frac{1}{^{52}C_{5}}$

Hence, the probability Luka correctly identifies all 5 cards in any order is  $\frac{1}{^{52}C_{5}}$.

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