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 are 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.)

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)

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

For the Coin

Sample Space ={Head, Tail}

n(S)=2

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

Since the events are independent,

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).

step-by-step explanation:

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question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!