Respuesta :
Answer:
The probability of drawing either 3 red cards or 3 face cards is 0.1276.
Step-by-step explanation:
Total number of card in standard deck is 52.
Number of red cards is 26.
Face card are king, queen and jack. Total number of face cards are [tex]3\times 4=12[/tex].
Formula of probability is
[tex]P=\frac{\text{Number of possible outcomes}}{\text{Total outcomes}}[/tex]
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Total outcomes is
[tex]^{52}C_3=\frac{52!}{3!(52-3)!}=22100[/tex]
Total possible outcomes of getting 3 red is
[tex]^{26}C_3=\frac{26!}{3!(26-3)!}=2600[/tex]
Total possible outcomes of getting 3 face is
[tex]^{12}C_3=\frac{12!}{3!(12-3)!}=220[/tex]
Total possible outcomes of getting either 3 black or 3 face cards is
[tex]2600+220=2820[/tex]
probability of drawing either 3 red cards or 3 face cards is
[tex]\frac{2820}{22100}=0.12760181\approx 0.1276[/tex]
probability of drawing either 3 red cards or 3 face cards is 0.1276.
Answer:
The probability of drawing either 3 red cards or 3 face cards is: 0.1267
Step-by-step explanation:
We are given a deck of 52 playing cards out of which we draw 3 cards.
We are asked to find the probability that the 3 card drawn are either 3 red cards or 3 face cards.
We know that in a playing cards we have 26 red cards and 12 face cards.
so we have to choose our card either from 26 red cards or 12 face cards and there are 6 cards which are both red card and is a face as well.
Let P denote the probability of an event.
Let A be the set that the card drawn is red.
B denote the set that the card drawn is a face card.
A∩B denote the set that the card drawn is red as well as is a face card.
We need to find the probability that the card drawn is either 3 red cards or 3 face cards i.e. we are asked to find P(A∪B)
We know that
P(A∪B)=P(A)+P(B)-P(A∩B)
Now [tex]P(A)=\dfrac{\binom{26}{3}}{\binom{52}{3}}[/tex]
[tex]P(B)=\dfrac{\binom{12}{3}}{\binom{52}{3}}[/tex]
[tex]P(A\bigcap B)=\dfrac{\binom{6}{3}}{\binom{52}{3}}[/tex]
Hence, [tex]P(A\bigcup B)=\dfrac{\binom{26}{3}}{\binom{52}{3}}+\dfrac{\binom{12}{3}}{\binom{52}{3}}-\dfrac{\binom{6}{3}}{\binom{52}{3}}[/tex]
[tex]P(A\bigcup B)=0.1267[/tex]
Hence, the probability of drawing either 3 red cards or 3 face cards is: 0.1267
