Answer :
Answer:
The probability that the first card will be a diamond, the second card will be a black card, and the third card will be a queen is 0.0096
Step-by-step explanation:
Total no. of cards = 52
No. of diamond cards = 13
No. of black cards = 26
No. of queens = 4
Three cards are drawn with replacement from a standard deck.
We are supposed to find he probability that the first card will be a diamond, the second card will be a black card, and the third card will be a queen
Probability of getting diamond card =[tex]\frac{13}{52}[/tex]
Probability of getting black card =[tex]\frac{26}{52}[/tex]
Probability of queen =[tex]\frac{4}{52}[/tex]
Probability that the first card will be a diamond, the second card will be a black card, and the third card will be a queen =[tex]\frac{13}{52} \times \frac{26}{52} \times \frac{4}{52}=0.0096[/tex]
Hence the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a queen is 0.0096
The probability that the first card be a diamond, the second card be a black card, and the third card be Queen is 0.0096.
What is probability?
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
Three cards are drawn with replacement from a standard deck.
Then the total card is 52.
Number of diamond cards = 13
Number of queen cards = 4
Number of black cards = 26
The probability that the first card will be a diamond card.
[tex]\rm P(D) = \dfrac{13}{52} = \dfrac{1}{4}[/tex]
The probability that the second card will be a black card.
[tex]\rm P(B) = \dfrac{26}{52} = \dfrac{1}{2}[/tex]
The probability that the third card will be a queen.
[tex]\rm P(Q) = \dfrac{4}{52} = \dfrac{1}{13}[/tex]
Then the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a queen will be
[tex]\rm P = \dfrac{1}{13} * \dfrac{1}{2} * \dfrac{1}{4} = \dfrac{1}{104} = 0.0096[/tex]
Thus, the probability is 0.0096.
More about the probability link is given below.
https://brainly.com/question/795909