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Gennadij [26K]
3 years ago
12

A fair die is cast, a fair coin is tossed, and a card is drawn from a standard deck of 52 playing cards. Assuming these events a

re independent, what is 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? (Round your answer to 4 decimal places.)
Mathematics
2 answers:
dem82 [27]3 years ago
7 0

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)

Stels [109]3 years ago
4 0

Answer:

0.0192 (Correct to 4 decimal places)

Step-by-step explanation:

<u>For the Fair Die</u>

Sample Space ={1,2,3,4,5,6}

n(S)=6

  • P(The uppermost part of the die is a 6), P(A) =\frac{1}{6}

<u>For the Coin</u>

Sample Space ={Head, Tail}

n(S)=2

  • P(The coin shows a head), P(B) =\frac{1}{2}

<u>For the Card </u>

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), P(C) =\frac{12}{52}

Since the events are independent,

P(A \cap B \cap C)=P(A) \cdot P(B) \cdot P(C)

=\frac{1}{6}X \frac{1}{2}X\frac{12}{52}\\=0.0192

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).

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