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Answer multiple choice questions based on independent and dependent events.
Questions and Answers
1.
In a class of 12 boys and 14 girls, Find P(Boy then boy without replacement)
A.
66/325
B.
17/38
C.
36/169
D.
4/13
Correct Answer A. 66/325
Explanation The probability of selecting a boy on the first draw is 12/26. After the first boy is selected, there are 11 boys left out of a total of 25 students. Therefore, the probability of selecting another boy on the second draw without replacement is 11/25. Multiplying these probabilities together gives (12/26) * (11/25) = 132/650, which simplifies to 66/325.
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2.
In a class of 12 boys and 14 girls, Find P(Girl then boy with replacement)
A.
1/2
B.
42/169
C.
77/325
D.
49/169
Correct Answer B. 42/169
Explanation The probability of selecting a girl and then a boy with replacement can be found by multiplying the probability of selecting a girl (14/26) by the probability of selecting a boy (12/26). This can be simplified to (14/26) * (12/26) = 168/676 = 42/169.
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3.
Using a standard deck of 52 cards, Find P(King then King without replacement)
A.
1/169
B.
4/663
C.
5/663
D.
1/221
Correct Answer D. 1/221
Explanation The probability of drawing a King from a standard deck of 52 cards is 4/52 since there are 4 Kings in the deck. After drawing the first King, there are only 51 cards left in the deck, and 3 Kings remaining. Therefore, the probability of drawing another King without replacement is 3/51. To find the probability of both events happening, we multiply the probabilities together: (4/52) * (3/51) = 1/221.
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4.
Using a standard deck of 52 cards, Find P(Ace then Jack with replacement)
A.
2/169
B.
1/13
C.
1/169
D.
4/663
Correct Answer C. 1/169
Explanation The probability of drawing an Ace from a standard deck of 52 cards is 4/52, since there are 4 Aces in the deck. After replacing the card, the probability of drawing a Jack is also 4/52. To find the probability of both events happening, we multiply the probabilities together: (4/52) * (4/52) = 16/2704 = 1/169. Therefore, the correct answer is 1/169.
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5.
If you roll a standard die and flip a coin, find P(5 then a tail)
A.
1/12
B.
5/12
C.
1/4
D.
1/8
Correct Answer A. 1/12
Explanation The probability of rolling a 5 on a standard die is 1/6, and the probability of flipping a tail on a coin is 1/2. Since the events of rolling a 5 and flipping a tail are independent, we can multiply the probabilities together to find the probability of both events occurring. Therefore, the probability of rolling a 5 and then flipping a tail is (1/6) * (1/2) = 1/12.