Calculating Probabilities in Binomial Experiments Quiz

  • 12th Grade
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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Questions: 20 | Updated: Jan 23, 2026
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1) What is P(X = 5)?

Explanation

(P(X=5)=C(10,5)/2^{10}=252/1024=63/256.)

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About This Quiz
Calculating Probabilities In Binomial Experiments Quiz - Quiz

Here, you'll calculate probabilities using the binomial distribution formula. This involves finding the probability of getting a specific number of successes in a fixed number of trials. Using real-world examples like coin flips, free throws, and quality control checks, you'll apply the binomial distribution formula to calculate probabilities for various... see moreoutcomes.
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2) What is P(X = 0)?

Explanation

(P(X=0)=(1/2)^{10}=1/1024.)

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3) What is P(X ≥ 8)?

Explanation

([C(10,8)+C(10,9)+C(10,10)]/2^{10}=(45+10+1)/1024=56/1024=7/128.)

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4) What is the most likely value of X?

Explanation

Mode ≈ floor((n+1)p)=floor(11×0.5)=5.

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5) What is P(X is even)?

Explanation

For a fair coin, P(even heads)=1/2.

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6) What is P(4 ≤ X ≤ 6)?

Explanation

(C(10,4)+C(10,5)+C(10,6))/2^{10}=(210+252+210)/1024=672/1024=21/32.)

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7) What is P(Y = 4)?

Explanation

Binomial: P(Y=4)=C(6,4)(0.7)^4(0.3)^2.

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8) What is P(Y = 0)?

Explanation

All misses: (0.3)^6.

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9) What is P(Y ≥ 5)?

Explanation

P(Y≥5)=P(5)+P(6)=C(6,5)(0.7)^5(0.3)+C(6,6)(0.7)^6.

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10) What is P(Y ≤ 2)?

Explanation

Sum k=0,1,2: C(6,0)(0.3)^6+C(6,1)(0.7)(0.3)^5+C(6,2)(0.7)^2(0.3)^4.

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11) What is the expected value E[Y]?

Explanation

E[Y]=np=6×0.7=4.2.

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12) Which is larger: P(Y = 3) or P(Y = 4)?

Explanation

Ratio P(4)/P(3)=(C(6,4)0.7^4 0.3^2)/(C(6,3)0.7^3 0.3^3)=(15/20)(0.7/0.3)=1.75>1.

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13) What is P(Z = 2)?

Explanation

Binomial: C(12,2)(0.1)^2(0.9)^{10}.

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14) What is P(Z ≥ 1)?

Explanation

1 - P(Z=0)=1-(0.9)^{12}.

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15) What is P(Z ≤ 3)?

Explanation

Sum probabilities for k=0,1,2,3.

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16) What is the most likely number of defectives (the mode)?

Explanation

Mode ≈ floor((n+1)p)=floor(13×0.1)=1.

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17) What is P(W = 3)?

Explanation

C(8,3)=56 and 8−3=5: 56(1/4)^3(3/4)^5.

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18) What is P(W = 0)?

Explanation

All 8 wrong: (3/4)^8.

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19) What is P(W ≥ 1)?

Explanation

1 - P(W=0)=1-(3/4)^8.

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20) Which is larger: P(W = 2) or P(W = 3)?

Explanation

Mode near (n+1)p=2.25 → k=2 more likely; inequality holds.

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What is P(X = 5)?
What is P(X = 0)?
What is P(X ≥ 8)?
What is the most likely value of X?
What is P(X is even)?
What is P(4 ≤ X ≤ 6)?
What is P(Y = 4)?
What is P(Y = 0)?
What is P(Y ≥ 5)?
What is P(Y ≤ 2)?
What is the expected value E[Y]?
Which is larger: P(Y = 3) or P(Y = 4)?
What is P(Z = 2)?
What is P(Z ≥ 1)?
What is P(Z ≤ 3)?
What is the most likely number of defectives (the mode)?
What is P(W = 3)?
What is P(W = 0)?
What is P(W ≥ 1)?
Which is larger: P(W = 2) or P(W = 3)?
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