Respuesta :
(a) Probability of getting a queen from a deck of 52 cards = [tex]\frac{1}{13}[/tex]
(b) Probability of getting a red card from a deck of 52 cards = [tex]\frac{1}{2}[/tex]
(c) Probability of getting a queen or a red card from a deck of 52 cards = [tex]\frac{7}{13}[/tex]
Solution:
Given that card is drawn from a standard deck of 52 cards.
Need to determine probability of getting
(a) queen (b) red (c) a queen or a red card
[tex]\text { Probability of an event }=\frac{\text { favorable number of events }}{\text { total number of events }}[/tex]
(a) Calculating probability of getting a queen from a deck of 52 cards
Favorable events are getting a queen of spade, heart , diamond or club.
Means number of favorable events = 4
Total events is all possible outcomes from 52 cards
So Total number of event = 52
[tex]\Rightarrow \text { probability of getting a queen }=\frac{4}{52}=\frac{1}{13}[/tex]
(b) Calculating probability of getting a red card from a deck of 52 cards
Number of red cards are 13 cards of diamonds and 13 cards of heart = 13+13 =26
So number of favorable event = 26
Total number of event = 52
[tex]\Rightarrow \text { probability of getting a red card }=\frac{26}{52}=\frac{1}{2}[/tex]
(c) Calculating probability of getting a queen or red card from a deck of 52 cards
Favorable events are 26 red cards + two queens of spade and club. Need to keep in mind that queens of heart and diamond is already considered in 26 red cards.
So number of favorable event = (26+2) = 28
Total number of event = 52
[tex]\text { Probability of getting a queen or red card }=\frac{28}{52}=\frac{7}{13}[/tex]
Summarizing the result :
(a) Probability of getting a queen from a deck of 52 cards = [tex]\frac{1}{13}[/tex]
(b) Probability of getting a red card from a deck of 52 cards = [tex]\frac{1}{2}[/tex]
(c) Probability of getting a queen or a red card from a deck of 52 cards = [tex]\frac{7}{13}[/tex]
