Question

A standard deck of cards contains 52 cards. One card is selected from the deck. ​(a) Compute the probability of randomly selecting a queen or two. ​(b) Compute the probability of randomly selecting a queen or two or king. ​(c) Compute the probability of randomly selecting a seven or diamond.

Answer 1

Let A be the event of selecting a queen; B be the event of selecting a two

a) There are 4 queens and 4 twos in a deck of 52 Hence P(A)=P(B)=4/52; Since A and B do not happen together P(AB)=0

Then by addition theorem P(A or B)= P(A)+P(B)-P(AB)=8/52

b) Let C be the event of selecting a king. P(C)=4/52. Again A, B, C are mutually exclusive ie they do not happen together

Hence P(AorBorC)=P(A)+P(B)+P(C)=12/52

c) Let D be the event of getting a diamond; E be the event of getting a 7. P(D)=13/52{13 diamonds in a deck}; P(E)= 4/52 Since there are 4 seven's in a deck; P(DE)=1/52( One among the 4 seven's will have the diamond sign)

Again applying addition theorem  P(D or E)= P(E)+P(D)-P(DE)=16/52