Content
Access custom-built, exam-style problems for distributions & random variables. Each problem has a full solution and mark-scheme, as well as AI grading and support.
Select a Difficulty:
7 / 39 problems visible - Upgrade to view all problems
!
0 / 4
On a penalty kick, Bob scores a goal 75% of the time. Over the course of a game, Bob kicks 8 penalty kicks.
Find the expected number of goals Bob scores during the game from penalty kicks.
Find the probability that Bob scores 8 goals.
Find the probability that Bob scores more than 5 goals.
!
0 / 6
A facial‑recognition access system is used to admit staff into a secure facility, but it is not perfectly reliable. When a registered employee presents themselves, there is a 15% chance the system will reject them. Each scan is independent of the others.
Twelve employees attempt entry and all are registered users.
Calculate the expected number of employees who will be granted access by the system.
Find the probability that exactly 3 of the 12 employees are rejected.
Determine the probability that fewer than 9 employees are granted access.
!
0 / 8
An electronics factory uses an automated inspection system to test non‑defective circuit boards. Each board has a 10% chance of being incorrectly rejected by the machine, and each test is independent.
A batch of 20 non‑defective boards is inspected.
Calculate the expected number of boards accepted by the system.
Find the probability that exactly 3 boards are wrongly rejected.
Determine the probability that at most 17 boards are accepted.
Compute the variance of the number of boards accepted.
0 / 6
0 / 9
0 / 6
0 / 13
Ask Plex AI about problem 4
Get hints, ask questions, and work through this problem step by step