Probability Quiz: Dependent Events

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| By Bheaton1

Bheaton1

Community Contributor

Quizzes Created: 2 | Total Attempts: 7,068

Questions: 10 | Attempts: 1,959 | Updated: Mar 21, 2023

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Students will find the probability of dependent events. MM1D2b

Questions and Answers

1.

There are 6 red, 4 green, 5 blue and 5 yellow marbles in a jar. What is the probability of picking a green marble, then a blue marble if you do not put back the first marble?
- A.
  
  1/20
- B.
  
  1/19
- C.
  
  9/20
- D.
  
  9/40
Correct Answer
B. 1/19

Explanation
Find the probability of picking green (4/20), then find the probability of picking blue (5/19). Remember there is one less marble in the jar.
Finally multiply the probabilities and reduce to get 1/19

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2.

There are 6 red, 4 green, 5 blue and 5 yellow marbles in a jar. What is the probability of picking a green marble, then a green marble if you do not put back the first marble?
- A.
  
  3/95
- B.
  
  4/95
- C.
  
  7/20
- D.
  
  1/25
Correct Answer
A. 3/95

Explanation
Find the probability of picking green (4/20), then find the probability of picking green again (3/19). Remember there is one less marble in the jar and that you assume the marble picked was green.
Finally multiply the probabilities and reduce to get 3/95

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2
0
3.

From a standard deck of playing cards, you pick a card and without returning the card you pick a second card. What is the probability that you picked a spade and then a heart?
- A.
  
  1/16
- B.
  
  1/2
- C.
  
  13/2704
- D.
  
  13/204
Correct Answer
D. 13/204

Explanation
Find the probability of picking a spade (13/52 or 1/4), then find the probability of picking a heart (13/51). Remember there is one less card.
Multiply the probabilities and reduce to get: 13/204

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1
1
4.

From a standard deck of playing cards, you pick a card and without returning the card you pick a second card. What is the probability that you picked a 10 and then a face card (king, queen or jack)?
- A.
  
  3/169
- B.
  
  12/663
- C.
  
  2/13
- D.
  
  1/221
Correct Answer
B. 12/663

Explanation
Find the probability of picking a 10 (4/52 or 1/13), then find the probability of picking a face card (12/51). Remember there is one less card.
Multiply the probabilities and reduce to get: 12/663

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0
1
5.

A teacher has a box of crayons that contains 6 red, 6 blue, 6 green and 6 purple crayons. Haily picks a crayon out of the box, then without putting that crayon back she picks a second crayon. What is the probability that the first crayon is purple and the second crayon is purple?
- A.
  
  1/16
- B.
  
  11/47
- C.
  
  5/92
- D.
  
  3/46
Correct Answer
C. 5/92

Explanation
First find the probability of picking a purple crayon (6/24 or 1/4), then find the probability that the second crayon is also purple (5/23). Both the numberator and denominator change because we are picking the same color and not returning the first crayon.
Multiply the probabilities together to get: 5/92 reduced

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2
0
6.

A teacher has a box of crayons that contains 6 red, 6 blue, 6 green and 6 purple crayons. Haily picks a crayon out of the box, then without putting that crayon back she picks a second crayon. What is the probability that the first crayon is red and the second crayon is green?
- A.
  
  1/16
- B.
  
  11/47
- C.
  
  5/92
- D.
  
  3/46
Correct Answer
D. 3/46

Explanation
First find the probability of picking a red crayon (6/24 or 1/4), then find the probability that the second crayon is green (6/23).
Multiply the probabilities together to get: 3/46 reduced

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7.

On a math test, 5 out of 30 students got an A. If three students are chosen at random without replacement, what is the probability that all three got an A on the test?
- A.
  
  1/406
- B.
  
  1/216
- C.
  
  1/4
- D.
  
  125/24360
Correct Answer
A. 1/406

Explanation
First find the probability of picking an A student (5/30 or 1/6), then find the probability of the second A student (4/29) and finally the third A student (3/28)
Multiply the probabilities together and reduce to get: 1/406

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2
0
8.

On a math test, 5 out of 30 students got an A. If two students are chosen at random without replacement, what is the probability that the first student did NOT get an A and the second student got an A on the test?
- A.
  
  5/36
- B.
  
  2/87
- C.
  
  1/36
- D.
  
  25/174
Correct Answer
D. 25/174

Explanation
First find the probability of picking NOT an A student (25/30 or 5/6), then find the probability of the second student is an A student (5/29)
Multiply the probabilities together and reduce to get: 25/174

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9.

All the letters of the alphabet are written on a piece of paper and placed in bag. A student draws out a letter without putting back the letter they draw a second letter. What is the probability of picking a vowel and then the letter B?

Correct Answer
1/130
5/650

Explanation
Probability of picking a vowel (5/26), Probability of picking the letter B (1/25)
Multiply the probabilities then reduce to get: (1/130)

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1
4 0
10.

From a standard deck of cards, you draw two cards without replacement. What is the probability you drew a 6 and then an ace?

Correct Answer
4/663
16/2652

Explanation
The probability you pick a is 4/52, the probability you then pick an ace is 4/51
Multiply the probabilities and reduce to get: 4/663

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1
4 2

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Current Version
Mar 21, 2023

Quiz Edited by
ProProfs Editorial Team
Oct 02, 2011

Quiz Created by
Bheaton1

Probability Quiz: Dependent Events

There are 6 red, 4 green, 5 blue and 5 yellow marbles in a jar. What is the probability of picking a green marble, then a blue marble if you do not put back the first marble?

There are 6 red, 4 green, 5 blue and 5 yellow marbles in a jar. What is the probability of picking a green marble, then a green marble if you do not put back the first marble?

From a standard deck of playing cards, you pick a card and without returning the card you pick a second card. What is the probability that you picked a spade and then a heart?

From a standard deck of playing cards, you pick a card and without returning the card you pick a second card. What is the probability that you picked a 10 and then a face card (king, queen or jack)?

A teacher has a box of crayons that contains 6 red, 6 blue, 6 green and 6 purple crayons. Haily picks a crayon out of the box, then without putting that crayon back she picks a second crayon. What is the probability that the first crayon is purple and the second crayon is purple?

A teacher has a box of crayons that contains 6 red, 6 blue, 6 green and 6 purple crayons. Haily picks a crayon out of the box, then without putting that crayon back she picks a second crayon. What is the probability that the first crayon is red and the second crayon is green?

On a math test, 5 out of 30 students got an A. If three students are chosen at random without replacement, what is the probability that all three got an A on the test?

On a math test, 5 out of 30 students got an A. If two students are chosen at random without replacement, what is the probability that the first student did NOT get an A and the second student got an A on the test?

All the letters of the alphabet are written on a piece of paper and placed in bag. A student draws out a letter without putting back the letter they draw a second letter. What is the probability of picking a vowel and then the letter B?

From a standard deck of cards, you draw two cards without replacement. What is the probability you drew a 6 and then an ace?