Question

Question 6 Unsaved

When randomly choosing two cards from a standard deck of cards without replacement, what is the probability of choosing a number card and then an ace? (Remember: standard deck has 52 cards, with 4 aces and 12 face cards)

Question 6 options:

12/221


3/169


4/221


9/169

 

Shironda rolls a number cube(six sides) and chooses a card from a standard deck of cards(52 cards). 

What is the probability that Shironda rolls an even number on the number cube and then chooses a black card from the deck?

Question 7 options: 1/21/41/8 1/13

Answer 1

Question (6)

To answer this question we will find out both probabilities one by one and then we will multiply both probabilities.

Probability of getting a number card from standard deck will be

`(9\cdot 4)/(52)=(36)/(52)`

Probability of getting one ace will be
`(4)/(51)` as we are given that second card is drawn without replacement.

To find the probability of choosing a number card and then an ace without replacement will be,

`=(4)/(51)\cdot (36)/(52)=(36)/(13\cdot 51)\\ \\ =(12)/(13\cdot 17)=(12)/(221)`

Therefore, first option is the correct choice.

Question (7)

Let us find out probability that Shironda will get an even number after rolling a cube. We know that a standard dice contains 3 even and 3 odd numbers.

Probability of getting an even number =
`(3)/(6)=(1)/(2)`.

Now let us find out probability of getting a black card from the deck.

Probability of getting a black card,

=
`(2\cdot 13)/(52)=(26)/(52)=(1)/(2)`

Now we can get probability of getting an even number and a black card by multiplying both probabilities.

`(1)/(2)\cdot (1)/(2)=(1)/(4)`

Therefore, probability of getting an even number and a black card is 1/4.