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:1/21/41/81/13

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

$\frac{9\cdot 4}{52}=\frac{36}{52}$

Probability of getting one ace will be $\frac{4}{51}$ 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,

$=\frac{4}{51}\cdot \frac{36}{52}=\frac{36}{13\cdot 51}\\ \\ =\frac{12}{13\cdot 17}=\frac{12}{221}$

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 = $\frac{3}{6}=\frac{1}{2}$.

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

Probability of getting a black card,

=$\frac{2\cdot 13}{52}=\frac{26}{52}=\frac{1}{2}$

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

$\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}$

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