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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 a 5 on the number cube and then chooses a 5 from the deck?

1/78
1/24
5/78
10/39

Respuesta :

kolbyregister
The answer is 178. Explanation:

The probability that one rows a 5 on a standard six-sided cube is 16 since there is 1 number on the dice that has the number 5 out of a total of 6 possibilities.

On a deck of 52 cards, there are four 5's (for each suit). Thus the probability is 452=113

These events are independent. Thus, to calculate their P(A and B), we multiply their probabilities. 16⋅113=178

Answer:  The correct option is (A) [tex]\dfrac{1}{78}.[/tex]

Step-by-step explanation:  Given that Shironda rolls a number cube with 6 sides and chooses a card from a standard deck of 52 cards.

We are to find the probability that Shironda rolls a 5 on the number cube and then chooses a 5 from the deck.

There is only one 5 in a number cube with 6 sides, so the probability of rolling a 5 on the number cube is

[tex]p_1=\dfrac{1}{6}.[/tex]

There are four 5's in a deck of 52 cards, so the probability of rolling a 5 from the deck is

[tex]p_2=\dfrac{4}{52}=\dfrac{1}{13}.[/tex]

Therefore,  the probability that Shironda rolls a 5 on the number cube and then chooses a 5 from the deck is given by

[tex]P=p_1\times p_2=\dfrac{1}{6}\times\dfrac{1}{13}=\dfrac{1}{78}.[/tex]

Thus, the required probability is [tex]\dfrac{1}{78}.[/tex]

Option (A) is CORRECT.