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A standard deck of 525252 cards contains 444 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 222 through 101010, a jack, a queen, a king, and an ace.Zhi Qing decides to pick one card at random from a standard deck of 525252 cards. Let AAA be the event that she chooses a three card and BBB be the event that she chooses a seven card.What is P(A\text{ or }B)P(A or B)P, (, A, start text, space, o, r, space, end text, B, ), the probability that the card Zhi Qing chooses is either a three or a seven?

User Nico Burns
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2 Answers

3 votes

The question seems a bit erroneous hence I am writing the correct question here and then answering it.

A standard deck of 52 cards contains 4 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 2 through 10, a jack, a queen, a king, and an ace. Zhi Qing decides to pick one card at random from a standard deck of 52 cards. Let A be the event that she chooses a three card and B be the event that she chooses a seven card. What is P(A or B), the probability that the card Zhi Qing chooses is either a three or a seven?

Answer:

The probability that the card Zhi Qing chooses is either a three or a seven is 8/52.

Explanation:

Event A: She chooses a three card. We can calculate the probability of event A as:

P(A) = No. of 3 numbered cards/Total no. of cards

Since there are 4 suits and each suit has 1 three-numbered card, so there are a total of 4 three-numbered cards.

P(A) = 4/52

Event B = She chooses a seven card. We can calculate the probability as:

P(B) = No. of seven-numbered cards/Total no. of cards

Again, there are 4 suits and each suit has 1 seven-numbered card. So, the number of 7-numbered cards is 4.

P(B) = 4/52

The probability that Zhi Qing chooses either a three or a seven is:

P(A or B) = P(A) + P(B) - P(A and B)

P(A and B) = 0 because a card can not be a seven and a 3 at the same time. These events are mutually exclusive hence P(A and B)is equal to zero. So,

P(A or B) = P(A) + P(B)

= 4/52 + 4/52

P(A or B) = 8/52

User Lars Brinkhoff
by
6.1k points
6 votes

Answer:

2/13

Explanation:

Number of Cards in a Deck, n(S)=52

A is the Event that she picked a three card.

n(A)=4

B is the Event that she picked a seven card.

n(B)=4

P(A)=n(A)/n(S)=4/52

P(B)=n(B)/n(S)=4/52

P(A or B)=P(A)+P(B)

=4/52+4/52

=8/52

=2/13

The probability that the card Zhi Qing chooses is either a three or a seven is 2/13.

User Ryanc
by
6.7k points
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