What is drawn at random from a well shuffled pack of 52 cards then the probability of that being a king is?

A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Open in App

From a well shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn isi Red and a kingii Either red or a king

Open in App

Text Solution

Solution : Let S be the sample space. Then, n(S) = 52. <br> Let `E_(1)` = event of getting a spade, <br> and `E_(2)` = event of getting a king. <br> Then, `(E_(1) nn E_(2)) =` event of getting a king of spades. <br> Clearly, `n(E_(1)) = 13, n(E_(2)) = 4 and n(E_(1) nn E_(2)) = 1.` <br> `therefore P(E_(1)) = (n(E_(1)))/(n(S)) = 13/52 = 1/4, P(E_(2)) = (n(E_(2)))/(n(S)) = 4/52 = 1/13.` <br> and `P(E_(1) nn E_(2)) = (n(E_(1) nn E_(2)))/(n(S)) = 1/52.` <br> `therefore` P(getting a spade or a king) <br> `= P(E_(1) or E_(2)) = P(E_(1) uu E_(2))` <br> `= P(E_(1)) + P(E_(2)) - P(E_(1) nn E_(2))` [by the addition theorem for two events] <br> `= (1/4 + 1/13 - 1/52) = 16/52 = 4/13.` <br> Hence, the required probability is `4/13`.