regis uses a fair deck of 52 different cards to determine the probability of drawing the same card twice in a row. he draws one card, replaces it, shuffles the deck, and draws another card. He records the results of the two draws.
how many outcomes are in the sample space?
The sample space is the set of all possible outcomes in an experiment. In this case, there are 52 different cards in the deck and Regis is drawing two cards with replacement, meaning that after each draw, he puts the card back into the deck before drawing the next card.
Since there are 52 cards in the deck, there are 52 possible outcomes for the first draw. After putting the first card back into the deck, there are still 52 cards to choose from for the second draw. Therefore, there are also 52 possible outcomes for the second draw.
To find the total number of outcomes in the sample space, we multiply the number of possible outcomes for the first draw (52) by the number of possible outcomes for the second draw (52):
Total outcomes = 52 × 52 = 2,704
Therefore, there are 2,704 outcomes in the sample space.
what is 3 5/7 divided by 7
To divide a mixed number by a whole number, you need to first convert the mixed number to an improper fraction.
To convert the mixed number 3 5/7 to an improper fraction, multiply the whole number (3) by the denominator of the fraction (7), then add the numerator (5) to get the numerator of the improper fraction. Keep the same denominator.
3 5/7 as an improper fraction is (3 x 7 + 5)/7 = 26/7.
Now, to divide 26/7 by 7, you can multiply the numerator (26) by the reciprocal of the denominator (7/1).
(26/7) ÷ 7 = (26/7) x (1/7) = 26/49
Therefore, 3 5/7 divided by 7 is equal to 26/49.
what is the estimate of 3 5/7 divided by 7
To estimate the division of 3 5/7 by 7, we can round the numbers to the nearest whole numbers and perform the division.
Rounding 3 5/7 to the nearest whole number gives us 4.
Rounding 7 to the nearest whole number gives us 7.
Now we can perform the division: 4 ÷ 7.
The quotient is approximately 0.571.
Therefore, the estimate of 3 5/7 divided by 7 is approximately 0.571.
The number of outcomes in the sample space can be calculated by multiplying the number of outcomes in the first draw by the number of outcomes in the second draw. Since Regis draws one card, replaces it, and shuffles the deck before drawing the second card, each draw is independent.
In the first draw, there are 52 possible outcomes, as all 52 cards can be drawn.
Similarly, in the second draw, there are also 52 possible outcomes.
Therefore, the total number of outcomes in the sample space is 52 multiplied by 52, which equals 2,704.
To determine the number of outcomes in the sample space, we need to consider each draw separately and multiply the number of possible outcomes for each draw.
In the first draw, Regis can select any of the 52 cards from the deck. Therefore, there are 52 possible outcomes for the first draw.
For the second draw, since Regis replaces the card back into the deck and shuffles it again, he still has 52 cards to choose from. Hence, there are 52 possible outcomes for the second draw as well.
To calculate the total number of outcomes in the sample space, we multiply the number of outcomes for each draw: 52 x 52 = 2,704.
Therefore, there are 2,704 outcomes in the sample space for Regis' experiment.