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SOPHIA STATISTICS UNIT III MILESTONE
Phil is randomly drawing cards from a deck of 52. He first draws a Queen, places it back in the deck, shuffles the deck, and then draws another card. What is the probability of drawing a Queen, placing it back in the deck, and drawing any face card? Answer choices are in the form of a percentage, rounded to the nearest whole number. 31% 2% 25% 7% RATIONALE Since Phil puts the card back and re-shuffles, the two events (first draw and second draw) are independent of each other. To find the probability of getting a Queen on the first draw and a face card on the second draw, we
can use the following formula: CONCEPT card is. "And" Probability for Independent Events I need help with this question Which of the following situations describes a continuous distribution? A probability distribution showing the amount of births in a hospital in a month A probability distribution showing the number of vaccines given to babies during their first year of life Note that the probability of drawing a Queen card is , while the probability of drawing a face
Since the test results indicate negatively, showing that the woman is not pregnant when in fact she is pregnant, this is a false negative. CONCEPT False Positives/False Negatives I need help with this question 21 Mark looked at the statistics for his favorite baseball player, Jose Bautista. Mark looked at seasons when Bautista played 100 or more games and found that Bautista's probability of hitting a home run in a game is 0.173. If Mark uses the normal approximation of the binomial distribution, what will be the variance of the number of home runs Bautista is projected to hit in 100 games? Answer choices are rounded to the tenths place.
RATIONALE In this situation, we know:
n = sample size = 100 p = success probability = 0. We can also say that q, or the complement of p, equals: q = 1 - p = 1 - 0.173 = 0. The variance is equivalent to npq: CONCEPT Normal Distribution Approximation of the Binomial Distribution I need help with this question Which of the following is a property of binomial distributions? The sum of the probabilities of successes and failures is always 1. All trials are dependent. The expected value is equal to the number of successes in the experiment. There are exactly three possible outcomes for each trial. RATIONALE Recall that for any probability distribution, the sum of all the probabilities must sum to 1. CONCEPT
Choose the correct probability of drawing a face card or an Ace. Answer choices are in the form of a percentage, rounded to the nearest whole number. 8% 4% 31% 25% RATIONALE Since the two events, drawing a face card and drawing an ace card, are non-overlapping, we can use the following formula: CONCEPT "Either/Or" Probability for Non-Overlapping Events I need help with this question 3 John is playing a game with a standard deck of playing cards. He wants to draw a jack on the first try.
Which of the following statements is true? The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack increases. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. The probability that John draws a jack on the first try is 3/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same.
RATIONALE
If we suppose that the card chosen by the magician is fixed, then there are 10 possible values, {6, 7, 8, 9, 10, 11, 12, 13, 14, or 15}, that are all equally likely. So, the probability that a specific value is chosen is: CONCEPT
Theoretical Probability/A Priori Method I need help with this question 5 Select the following statement that describes non-overlapping events. Receiving the Queen of Diamonds fulfills Luke's need of getting both a face card and a diamond. Luke wants a red card so he can have a winning hand, and he receives the five of clubs. Luke needs to roll an odd number to win. When it’s his turn, he rolls a five. To win, Luke needs a black card. He receives an eight of spades. RATIONALE Events are non-overlapping if the two events cannot both occur in a single trial of a chance experiment. Since he wants a red card {Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, or King: In either Diamond or Hearts} and he got the Five of Clubs, there is no overlap. CONCEPT Overlapping Events I need help with this question 6
Tails, One RATIONALE Recall a coin has heads and tails and a standard die has six values, {1, 2, 3, 4, 5, or 6}. So, obtaining a value of 7 is not possible. CONCEPT Outcomes and Events I need help with this question 7 Asmita went to a blackjack table at the casino. At the table, the dealer has just shuffled a standard deck of 52 cards. Asmita has had good luck at blackjack in the past, and she actually got three blackjacks with Aces in a row the last time she played. Because of this lucky run, Asmita thinks that Ace is the luckiest card. The dealer deals the first card to her. In a split second, she can see that it is a non-face card, but she is unsure if it is an Ace. What is the probability of the card being an Ace, given that it is a non-face card? Answer choices are in a percentage format, rounded to the nearest whole number. 8% 77% 69%
RATIONALE
The probability of it being an Ace given it is a Non-face card uses the conditional formula: Note, that in a standard deck of 52 cards, there are 12 face cards, so 40 non-face cards. Of those non-face cards, there are only 4 Aces. CONCEPT
a spade, given that the first card was also a spade, would be because we now have only 11 cards remaining and only two of those cards are spades (since the first card was a spade). So we can use these probabilities to find the probability that the two cards will both be spades: CONCEPT "And" Probability for Dependent Events I need help with this question 9
David is playing a game where he flips two coins and counts the total number of heads. The possible outcomes and probabilities are shown in the probability distribution below. What is the expected value for the number of heads from flipping two coins? 1 2 3
RATIONALE The expected value, also called the mean of a probability distribution, is found by adding the products of each individual outcome and its probability. We can use the following formula to calculate the expected value, E(X):
RATIONALE
To get the probability of A given B has occurred, we can use the following conditional formula: The probability of A and B is the intersection, or overlap, of the Venn diagram, which is 0.1. The probability of B is all of Circle B, or 0.1 + 0.35 = 0.45. CONCEPT Conditional Probability
I need help with this question 11 The average number of tunnel construction projects that take place at any one time in a certain state is 3. Find the probability of exactly five tunnel construction projects taking place in this state.
