Three cards are drawn with replacement from a standard deck. What is the probability that the first card will be a spade, the second card will be a black card, and the third card will be a queen? Write your answer as a fraction or a decimal number rounded to three decimal places.
since you replace, then each trial is independent of the others.
1/4 * 1/2 * 4/52 = .0096153846
=.010 to three decimal place
or .00962 to three significant figures
Three cards are drawn with replacement from a standard deck. What is the probability that the first card will be a club, the second card will be a black card, and the third card will be an ace? Express your answer as a fraction or a decimal number rounded to four decimal places.
To calculate the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
1. Number of favorable outcomes:
The first card must be a spade, and there are 13 spades in a standard deck. Therefore, the number of favorable outcomes for the first card is 13.
2. Total number of possible outcomes:
There are 52 cards in a standard deck, and since we are drawing with replacement, the total number of possible outcomes for each card is still 52.
Now, let's calculate the probability.
P(First card is a spade) = Number of favorable outcomes / Total number of possible outcomes
P(First card is a spade) = 13 / 52 = 1/4
P(Second card is a black card) = Number of favorable outcomes / Total number of possible outcomes
Since half of the deck is black, the number of favorable outcomes is 26.
P(Second card is a black card) = 26 / 52 = 1/2
P(Third card is a queen) = Number of favorable outcomes / Total number of possible outcomes
There are 4 queens in a standard deck, so the number of favorable outcomes is 4.
P(Third card is a queen) = 4 / 52 = 1/13
To calculate the probability that all three events occur, we multiply the probabilities of each event:
P(First card is a spade, second card is black, third card is a queen) = P(First card is a spade) * P(Second card is a black card) * P(Third card is a queen)
P(First card is a spade, second card is black, third card is a queen) = (1/4) * (1/2) * (1/13) = 1/104
Therefore, the probability that the first card will be a spade, the second card will be a black card, and the third card will be a queen is 1/104 or approximately 0.0096 (rounded to three decimal places).
To find the probability of drawing a specific sequence of cards, we need to find the probability of each individual event and multiply them together.
Step 1: Determine the probability of drawing a spade as the first card.
In a standard deck of 52 cards, there are 13 spades. Since we're drawing with replacement, the probability of drawing a spade on the first draw is 13/52, which simplifies to 1/4.
Step 2: Determine the probability of drawing a black card as the second card.
There are 26 black cards (clubs and spades) in a standard deck. After drawing the first card, there are still 52 cards in the deck since we are drawing with replacement. Therefore, the probability of drawing a black card on the second draw is 26/52, which simplifies to 1/2.
Step 3: Determine the probability of drawing a queen as the third card.
There are 4 queens in a standard deck. After drawing the first and second cards, there are still 52 cards in the deck. Therefore, the probability of drawing a queen on the third draw is 4/52, which simplifies to 1/13.
Step 4: Multiply the probabilities from each step together.
Probability(first card is a spade) × Probability(second card is black) × Probability(third card is a queen) = (1/4) × (1/2) × (1/13) = 1/104.
Therefore, the probability that the first card will be a spade, the second card will be a black card, and the third card will be a queen is 1/104.