Probability & Expected Value Revision
Authored by Benjamin Simpson-Court
Mathematics
11th - 12th Grade
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7 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The probability of an event can be a negative number.
Answer explanation
Probability values always range from 0 (impossible) to 1 (certain)
2.
FILL IN THE BLANKS QUESTION
1 min • 1 pt
If the probability of rain tomorrow is 0.3, the probability of it not raining is (a) .
Answer explanation
The sum of probabilities for an event happening and not happening is 1.
So, P(not rain) = 1 - P(rain) = 1 - 0.3 = 0.7
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does 'Expected Value' primarily help us understand?
The most likely single outcome.
The average outcome if a situation is repeated many times.
The guaranteed profit or loss.
The simplest way to calculate probability.
Answer explanation
Expected value represents a long-term average outcome, not a prediction for a single event.
4.
MATH RESPONSE QUESTION
2 mins • 1 pt
A game involves rolling a fair six-sided die.
You win £12 if you roll a 6, and £0 otherwise.
What is the expected value of playing this game once? (Enter numbers only, e.g., 2.50)
Mathematical Equivalence
ON
Answer explanation
P(rolling a 6) = 1/6. P(not rolling a 6) = 5/6.
Expected Value = (£12 1/6) + (£0 5/6) = £2 + £0 = £2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
On a probability tree diagram, if one branch has a probability of 0.5 and a subsequent branch connected to it has a probability of 0.4, what is the probability of following both these branches in sequence?
0.9
0.1
0.2
0.02
Answer explanation
To find the probability of a sequence of events on a tree diagram, you multiply the probabilities along the branches: 0.5 * 0.4 = 0.2
6.
DROPDOWN QUESTION
1 min • 1 pt
To make a decision between two financial options based on probability, we typically choose the option with the (a) expected profit, or the (b) expected cost.
Answer explanation
We aim to maximize expected profit or minimize expected cost.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If an insurance policy has a positive expected value for the insurance company, it generally has a negative expected value for the person buying the policy (when only considering financial outcomes).
Answer explanation
For the insurance company to make a profit on average, the premiums collected must be greater than the expected payouts. This means, on average, the policyholder pays more than they expect to receive in claims.
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