Respuesta :
Answer:
52 cards in a standard deck
26 cards are red two of these are jacks
26 + 2 ( black jacks)
probability is 28/52
The probability of drawing a Jack or a red card from a standard deck of playing cards is 7/13
What is probability?
"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:
[tex]P(A)=\frac{n(A)}{n(S)}[/tex]
where [tex]n(A)[/tex] is the number of favorable outcomes
[tex]n(S)[/tex] is the total number of events in the sample space.
Formula to find the probability of event A or event B:
P(A∪B) = P(A) + P(B) - P(A∩B)
For given question,
Sample is a standard deck of 52 playing cards.
⇒ [tex]n(S)=52[/tex]
Let event A: drawing a Jack from a standard deck of playing cards
event B: drawing a red card from a standard deck of playing cards
For event A, as there are 4 Jack in a standard deck of cards
[tex]n(A)=4[/tex]
So, the probability of drawing a Jack
⇒ [tex]P(A)=\frac{n(A)}{n(S)}[/tex]
⇒ [tex]P(A)=\frac{4}{52}[/tex]
For event B, as there are 26 red cards in a deck of cards
[tex]n(B)=26[/tex]
So, the probability of drawing red card is
⇒ [tex]P(B)=\frac{n(B)}{n(S)}[/tex]
⇒ [tex]P(B)=\frac{26}{52}[/tex]
Let, A∩B represents the common cards. As there are two red Jack cards in a standard deck of cards, [tex]n(A\cap B)=2[/tex]
So, the probability of drawing red Jack card is,
⇒ [tex]P(A\cap B)=\frac{n(A\cap B)}{n(S)}[/tex]
⇒ [tex]P(A\cap B)=\frac{2}{52}[/tex]
Now, the probability of drawing a Jack or a red card from a standard deck of playing cards is P(A∪B)
⇒ [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
⇒ [tex]P(A\cup B)=\frac{4}{52} + \frac{26}{52} - \frac{2}{52}[/tex]
⇒ [tex]P(A\cup B)=\frac{28}{52}[/tex]
⇒ [tex]P(A\cup B)=\frac{7}{13}[/tex]
Hence, the probability of drawing a Jack or a red card from a standard deck of playing cards [tex]P(A\cup B)=\frac{7}{13}[/tex]
Learn more about Probability here:
https://brainly.com/question/11234923
#SPJ2
