Respuesta :
Answer:
The probability is 0.0192 to four decimal places.
Step-by-step explanation:
In this question, we are asked to calculate the probabilities that three events will occur at the same time.
Firstly, we identify the individual probabilities.
The probability of 6 showing In a throw of die is 1/6
The probability of a coin showing head in a flip of coin is 1/2
The probability of a face card being drawn in a deck of cards is 12/52( There are 12 face cards in a deck of cards)
Mathematically to get the probability of all these events happening, we simply multiply all together.
This will be ;
1/6 * 1/2 * 12/52 = 1/52 = 0.0192 ( to 4 decimal place)
Answer:
0.0192 (Correct to 4 decimal places)
Step-by-step explanation:
For the Fair Die
Sample Space ={1,2,3,4,5,6}
n(S)=6
- P(The uppermost part of the die is a 6), [tex]P(A) =\frac{1}{6}[/tex]
For the Coin
Sample Space ={Head, Tail}
n(S)=2
- P(The coin shows a head), [tex]P(B) =\frac{1}{2}[/tex]
For the Card
n(S)=52 Cards
So, there are 13 cards of each suit. Among these 13 cards, there are 3 picture cards or face cards as they are called. These are the Jack, Queen and King cards.
Number of Picture Cards =12
- P(The card drawn is a picture card), [tex]P(C) =\frac{12}{52}[/tex]
Since the events are independent,
[tex]P(A \cap B \cap C)=P(A) \cdot P(B) \cdot P(C)[/tex]
[tex]=\frac{1}{6}X \frac{1}{2}X\frac{12}{52}\\=0.0192[/tex]
Therefore, the probability that the number falling on the uppermost part of the die is a 6, the coin shows a head, and the card drawn is a face card is 0.0192 (Correct to 4 decimal places).
