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?

Asked by Aaryan | 1 year ago |  28

##### Solution :-

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

By using the formula,

P (E) = $$\dfrac{favourable\; outcomes }{total\; possible\; outcomes}$$

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) = 4C148C= 778320

P (E) =$$\dfrac{ n (E) }{ n (S)}$$

= $$\dfrac{ 778320} { 2598960}$$

= $$\dfrac{ 3243}{10829}$$

(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+4C448C= 886656

P (E) =$$\dfrac{ n (E) }{ n (S)}$$

=$$\dfrac{ 886656 }{ 2598960}$$

= $$\dfrac{ 18472}{54145}$$

Answered by Aaryan | 1 year ago

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