Luis draws 1 card from a deck, 39 times. Predict how many times he draws an ace.
John and O'Neal are playing a board game in which they roll two number cubes. John needs to get a sum of 8 on the number cubes to win. O'Neal needs a sum of 11, if they take turns rolling the number cube, who is more likely to win? Explain.
Horace is going to roll a standard number cube and flip a coin. He wonders if it is more likely that he rolls a 5 and the coin lands on heads, or that he rolls a 5 or the coin lands on heads. Which event do you think is more likely to happen? Find the probability of both events to justify or reject your initial prediction.
Pierre asks Sherry a question involving the theoretical probability of a compound event in which you flip a coin and draw a marble from a bag of marbles. The bag of marbles coins 3 white marbles, 8 green marbles, and 9 black marbles. Sherry's answer, which is correct, is 12/40. What was Pierre's question?
Assuming the card is returned after each draw,
number = (4/52)(39)
= 3
To get an 8:
2,6
3,5
4,4
5,3
6,2
prob of getting an 8 = 5/36
to get 11:
5,6
6,5
prob of 11 = 2/36
compare
Second-last one makes no sense
What is the prob of getting a head on the coin and either a white or green marble ?
prob = (1/2)(12/20)
= 3/10, which is what the given answer should have been reduced to
To predict how many times Luis will draw an ace, we need to consider that there are 4 aces in a standard deck of 52 cards. The probability of drawing an ace on one draw is 4/52.
Therefore, the expected number of times Luis will draw an ace can be calculated as follows:
Expected number of aces = Probability of drawing an ace * Number of draws
Expected number of aces = (4/52) * 39 = 3
Therefore, it is predicted that Luis will draw an ace approximately 3 times.
In the case of John and O'Neal playing the board game, we need to examine the possible outcomes of rolling two number cubes and check how many times a sum of 8 or 11 can occur.
For John:
The possible outcomes that sum up to 8 are: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). There are 5 possible outcomes.
For O'Neal:
The possible outcomes that sum up to 11 are: (5, 6) and (6, 5). There are 2 possible outcomes.
Since John has 5 possible outcomes while O'Neal has only 2 possible outcomes, John is more likely to win the game.
For Horace rolling a standard number cube and flipping a coin, we need to calculate the probability for each event.
The probability of rolling a 5 on a number cube is 1/6, and the probability of the coin landing on heads is 1/2.
The probability of both events happening is calculated by multiplying the individual probabilities together:
Probability of rolling a 5 and coin landing on heads = (1/6) * (1/2) = 1/12
The probability of either event happening is calculated by adding the individual probabilities minus the probability of both events occurring:
Probability of rolling a 5 or coin landing on heads = (1/6) + (1/2) - (1/12) = 7/12
Therefore, the event of either rolling a 5 or the coin landing on heads is more likely to happen with a probability of 7/12.
As for Pierre's question to Sherry, we can deduce that Pierre asked about the probability of the compound event involving flipping a coin and drawing a marble from a bag.
The bag has a total of 3 white marbles, 8 green marbles, and 9 black marbles, making a total of 20 marbles.
Sherry's answer of 12/40 suggests that the question was about the probability of drawing a white marble or flipping heads.
To calculate the theoretical probability, we consider the number of favorable outcomes (drawing a white marble or flipping heads) divided by the total number of possible outcomes (total marbles in the bag and two possible coin outcomes).
Therefore, Pierre's question was likely: "What is the probability of drawing a white marble or flipping heads?"
The probability of drawing a white marble is 3/20 and the probability of flipping heads is 1/2.
The probability of either event occurring is calculated by adding the individual probabilities and subtracting the probability of both events happening:
Probability of drawing a white marble or flipping heads = (3/20) + (1/2) - (3/20 * 1/2) = 12/40.
Therefore, Sherry's answer of 12/40 was correct.
To predict the number of times Luis draws an ace, we need to know the total number of cards in the deck and the number of aces in the deck. Let's assume we have a standard deck of 52 playing cards, which includes 4 aces.
To calculate the probability of drawing an ace in one draw, we divide the number of aces (4) by the total number of cards (52):
Probability of drawing an ace in one draw = Number of aces / Total number of cards = 4/52
Since Luis draws from the deck 39 times, we can use the concept of independent events to find the expected number of times he draws an ace. The expected number is calculated by multiplying the probability of success (drawing an ace) in one trial by the number of trials:
Expected number of times drawing an ace = Probability of drawing an ace in one draw * Number of trials = (4/52) * 39 = 3
Therefore, we predict that Luis will draw an ace approximately 3 times.
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To determine who is more likely to win in the game between John and O'Neal, we need to analyze the possible outcomes of rolling two number cubes. Each cube has numbers 1 to 6.
To win, John needs a sum of 8, so we consider all possible combinations that add up to 8: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). That gives us a total of 5 successful outcomes.
O'Neal needs a sum of 11, so we consider all possible combinations that add up to 11: (5, 6) and (6, 5). That gives us 2 successful outcomes.
Since John has 5 successful outcomes compared to O'Neal's 2 in the sample space of two dice rolls, we can conclude that John is more likely to win.
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To determine which event is more likely to happen for Horace, we need to consider the probabilities of rolling a 5 and flipping a coin for each event.
The probability of rolling a 5 on a standard number cube is 1/6 since there are 6 possible outcomes (numbers 1 to 6) and only one of them is a 5.
The probability of flipping a coin and getting heads is 1/2 since there are 2 possible outcomes (heads or tails) and only one of them is heads.
Now let's compare the probability of both events:
Probability of rolling a 5 and getting heads = (1/6) * (1/2) = 1/12
Probability of rolling a 5 or getting heads = (1/6) + (1/2) = 1/6 + 1/2 = 1/6 + 3/6 = 4/6 = 2/3
Based on the probabilities, we can see that the event of rolling a 5 or getting heads (2/3) is more likely to happen than rolling a 5 and getting heads (1/12).
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Without more information about the specific question Pierre asked Sherry, it is not possible to determine the exact wording of the question. However, based on Sherry's correct answer of 12/40, we can infer some possibilities.
One possible question Pierre might have asked is: "What is the probability of flipping a coin and drawing a white marble from the bag?"
To calculate the probability, we need to consider two independent events: flipping a coin (which has 2 equally likely outcomes: heads or tails) and drawing a white marble from a bag (which has 3 white marbles out of 20 total marbles).
Probability of flipping a coin and drawing a white marble = (1/2) * (3/20) = 3/40
However, since Sherry's answer was 12/40, which is 3 times larger, it suggests that the question may have involved repeating the compound event multiple times or considering all possible outcomes with the given information. Without more context, it is not possible to determine the exact question Pierre asked.
you stupid
if you dont kow this