Question

A deck of cards has 52 cards. There are 4 suits: diamonds, hearts, clubs, and spades. Each suit has 13 cards. What is the probability that I will randomly pick up 6 and then randomly pick a queen?

Answer 1

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Step-by-step explanation:

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`\Large \text{$ \sf P(A\:and\:B) = (4)/(52) * (4)/(51)$}`

`\Large \text{$ \sf P(A\:and\:B) = (16 / 4)/(2,652 / 4)$}`

`\Large \boxed{\boxed{\text{$ \sf P(A\:and\:B) = (4)/(663)$}}}`

Answer 2

The probability of first picking a six and then a queen from a standard deck of 52 cards is 4/663 after multiplying the independent probabilities of each event.

Step-by-step explanation:

The subject of this question is probability, which comes under the field of Mathematics. You are looking to find the probability of selecting a six and then a queen from a standard deck of 52 cards. Since these are two separate events, you need to find the probability of each event occurring and then multiply them together to find the overall probability.

For the first event, picking a six, there are 4 sixes in a 52-card deck (one for each suit). So the probability of picking a six (event 1) is:

Probability(Event 1) = Number of sixes / Total number of cards = 4/52 = 1/13

Upon picking a six, you are left with 51 cards. There are 4 queens in a deck of cards, so the probability of picking a queen (event 2) is:

Probability(Event 2) = Number of queens / Remaining number of cards = 4/51

Finally, to find the combined probability, you multiply the probabilities of event 1 and event 2 together:

Overall Probability = Probability(Event 1) * Probability(Event 2) = (1/13) * (4/51) = 4/663

Therefore, the probability of first picking a six and then a queen is 4/663.