MATH SOLVE

4 months ago

Q:
# Question 6 UnsavedWhen 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 3/1694/2219/169 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

Accepted Solution

A:

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[tex]\frac{9\cdot 4}{52}=\frac{36}{52}[/tex]Probability of getting one ace will be [tex]\frac{4}{51}[/tex] 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,[tex]=\frac{4}{51}\cdot \frac{36}{52}=\frac{36}{13\cdot 51}\\
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=\frac{12}{13\cdot 17}=\frac{12}{221}[/tex]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 = [tex]\frac{3}{6}=\frac{1}{2}[/tex].Now let us find out probability of getting a black card from the deck.Probability of getting a black card,=[tex]\frac{2\cdot 13}{52}=\frac{26}{52}=\frac{1}{2}[/tex]Now we can get probability of getting an even number and a black card by multiplying both probabilities.[tex]\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}[/tex]Therefore, probability of getting an even number and a black card is 1/4.