Calculating Probabilities in Binomial Experiments Quiz

  • Grade 12th
Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 11119 | Total Attempts: 9,762,531
| Attempts: 13 | Questions: 20 | Updated: Jan 23, 2026
Please wait...
Question 1 / 21
🏆 Rank #-- ▾
0 %
0/100
Score 0/100

1) 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.)

Submit
Please wait...
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.
see less

2)

What first name or nickname would you like us to use?

You may optionally provide this to label your report, leaderboard, or certificate.

2) What is P(W ≥ 1)?

Explanation

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

Submit

3) What is P(W = 3)?

Explanation

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

Submit

4) What is P(Z ≤ 3)?

Explanation

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

Submit

5) 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.

Submit

6) 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.

Submit

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

Explanation

E[Y]=np=6×0.7=4.2.

Submit

8) 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.

Submit

9) What is P(Z = 2)?

Explanation

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

Submit

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

Explanation

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

Submit

11) What is P(X = 5)?

Explanation

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

Submit

12) What is P(W = 0)?

Explanation

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

Submit

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

Explanation

Mode ≈ floor((n+1)p)=floor(13×0.1)=1.

Submit

14) What is P(Z ≥ 1)?

Explanation

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

Submit

15) What is P(Y = 0)?

Explanation

All misses: (0.3)^6.

Submit

16) What is P(Y = 4)?

Explanation

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

Submit

17) 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.)

Submit

18) What is P(X is even)?

Explanation

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

Submit

19) What is the most likely value of X?

Explanation

Mode ≈ floor((n+1)p)=floor(11×0.5)=5.

Submit

20) What is P(X = 0)?

Explanation

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

Submit
×
Saved
Thank you for your feedback!
View My Results
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
What is P(X ≥ 8)?
What is P(W ≥ 1)?
What is P(W = 3)?
What is P(Z ≤ 3)?
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)?
Which is larger: P(W = 2) or P(W = 3)?
What is P(X = 5)?
What is P(W = 0)?
What is the most likely number of defectives (the mode)?
What is P(Z ≥ 1)?
What is P(Y = 0)?
What is P(Y = 4)?
What is P(4 ≤ X ≤ 6)?
What is P(X is even)?
What is the most likely value of X?
What is P(X = 0)?
play-Mute sad happy unanswered_answer up-hover down-hover success oval cancel Check box square blue
Alert!