Five cards are drawn from a pack of 52 cards. What is the chance that

1.	Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain:(i) just one ace(ii) at least one ace?
Answer» Given: Five cards are drawn from a pack of 52 cards. By using the formula, P (E) = favourable outcomes / total possible outcomes Five cards are drawn at random, Total possible outcomes are ⁵²C₅ n (S) = 2598960 (i) Let E be the event that exactly only one ace is present n (E) = ⁴C₁⁴⁸C₄= 778320 P (E) = n (E) / n (S) = 778320 / 2598960 = 3243/10829 (ii) Let E be the event that at least one ace is present E = {1 or 2 or 3 or 4 ace(s)} n (E) = ⁴C₁⁴⁸C₄+ ⁴C₂⁴⁸C₃+ ⁴C₃⁴⁸C₂+ ⁴C₄⁴⁸C₁= 886656 P (E) = n (E) / n (S) = 886656 / 2598960 = 18472/54145

Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain:(i) just one ace(ii) at least one ace?

Answer»

Given: Five cards are drawn from a pack of 52 cards.

By using the formula,

P (E) = favourable outcomes / total possible outcomes

Five cards are drawn at random,

Total possible outcomes are ⁵²C₅

n (S) = 2598960

(i) Let E be the event that exactly only one ace is present

n (E) = ⁴C₁⁴⁸C₄= 778320

P (E) = n (E) / n (S)

= 778320 / 2598960

= 3243/10829

(ii) Let E be the event that at least one ace is present

E = {1 or 2 or 3 or 4 ace(s)}

n (E) = ⁴C₁⁴⁸C₄+ ⁴C₂⁴⁸C₃+ ⁴C₃⁴⁸C₂+ ⁴C₄⁴⁸C₁= 886656

P (E) = n (E) / n (S)

= 886656 / 2598960

= 18472/54145

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