Probability & Expected Value Revision

The probability of an event can be a negative number.

• True
• False

Answer explanation

Probability values always range from 0 (impossible) to 1 (certain)

If the probability of rain tomorrow is 0.3, the probability of it not raining is _____.

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

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.

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

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

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.

• higher
• lower
• equal
• average
• maximum

Answer explanation

We aim to maximize expected profit or minimize expected cost.

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).

• True
• False

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.