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Question

A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card.


Solution

Let S be the sample space. Then, n(S) = 52.

Let E1,E2 and E3 be the events of getting a king, a heart and a red card respectivel. Then,

n(E1)=4,n(E2)=13 and n(E3)=26.

(E1E2) = event of getting a king of hearts;

(E2E3) = event of getting a heart            [ a heart is a red card also];

(E3E1) = event of getting a red king;

and (E1E2E3) = event of getting a king of hearts.

n(E1E2)=1,n(E2E3)=13,n(E3E1)=2 and n(E1E2E3)=1.

P(E1)=n(E1)n(S)=452=113;P(E2)=n(E2)n(S)=1352=14;

P(E3)=n(E3)n(S)=2652=12;P(E1E2)=n(E1E2)n(S)=152;

P(E2E3)=n(E2E3)n(S)=252=126

and P(E1E2E3)=n(E1E2E3)n(S)=152.

P(getting a king or a heart or a red card)

P(getting a king or a heart or a red card)

=P(E1 or E2 or E3)=P(E1E2E3)

=P(E1)+P(E2)+P(E3)P(E1E2)P(E2E3)P(E3E1)+P(E1E2E3)

=(113+14+1215214126+152)=2852=713.

Hence, the required probability is 713.


Mathematics

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