Question

1. a card flip. for each of the given tasks, randomly pick a single card from a standard deck and proceed as per the task shown. express your answer as a reduced fraction.

find the probability that your card is

part 1 of 8
(1) the 4 of clubs.
the probability that the first card picked up was a 4 of clubs is

part 2 of 8
(2) a black card.
the probability that the first card picked up was a black card is

part 3 of 8
(3) a queen.
the probability that the first card picked up was a queen is

part 4 of 8
(4) a black 10.
the probability that the first card picked up was a black 10 is

part 5 of 8
(5) a red card or a 5.
the probability that the first card picked up was a red card or a 5 is

part 6 of 8
(6) a club and a 4.
the probability that the first card picked up was a club and a 4 is

part 7 of 8
(7) a 7 or an ace.
the probability that the first card picked up was a 7 or an ace is

part 8 of 8
(8) a club, diamond, or spade.
the probability that the first card picked up was a club, diamond, or spade is

Explanation:

Step1: Count total number of cards

A standard deck has \(52\) cards.

Step2: Count number of clubs, diamonds, or spades

Clubs (\(13\)), diamonds (\(13\)), spades (\(13\)). Total \(13 + 13+13=39\) cards.

Step3: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{39}{52}\). Simplify \(\frac{39\div13}{52\div13}=\frac{3}{4}\).

Answer:

\(\frac{3}{4}\)