Independent And Dependent Events Day 2

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| By Etjersland

Etjersland

Community Contributor

Quizzes Created: 3 | Total Attempts: 6,354

Questions: 5 | Attempts: 577 | Updated: Mar 21, 2023

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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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1
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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.

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Current Version
Mar 21, 2023

Quiz Edited by
ProProfs Editorial Team
Feb 24, 2010

Quiz Created by
Etjersland

Independent And Dependent Events Day 2

In a class of 12 boys and 14 girls, Find P(Boy then boy without replacement)

In a class of 12 boys and 14 girls, Find P(Girl then boy with replacement)

Using a standard deck of 52 cards, Find P(King then King without replacement)

Using a standard deck of 52 cards, Find P(Ace then Jack with replacement)

If you roll a standard die and flip a coin, find P(5 then a tail)