C955 Applied Probability and Statistics - Set 1 - Part 2

Correct Answer: An experiment applies a treatment while an observational study only observes

In an experiment researchers actively assign treatments, allowing causal conclusions. Observational studies record what occurs naturally and generally support only association.

Correct Answer: A third variable or reverse causation may explain the association

An observed association may arise from a confounding variable affecting both, from reverse causation, or from coincidence, so correlation alone cannot establish cause.

Correct Answer: An outside variable related to both the explanatory and response variables

A confounder is associated with both the presumed cause and the effect, creating a spurious association that can be mistaken for a causal relationship.

Correct Answer: Balancing known and unknown confounders across treatment groups

Random assignment distributes confounding variables evenly across groups on average, so differences in outcome can be attributed to the treatment.

Correct Answer: Providing a comparison baseline against which to judge the treatment effect

The control group experiences everything except the active treatment, isolating the treatment's effect from other influences on the outcome.

Correct Answer: Improvement resulting from the expectation of treatment rather than the treatment itself

Participants may improve simply because they believe they received treatment, which is why blinded designs with placebo controls are used.

Correct Answer: Neither participants nor those assessing outcomes know the group assignments

Double-blinding conceals assignment from both participants and evaluators, preventing expectations from influencing either reported or assessed outcomes.

Correct Answer: The event cannot occur

Probabilities range from 0 to 1. A probability of 0 means the event is impossible, and 1 means it is certain.

Correct Answer: 0.5

A fair coin has two equally likely outcomes, so the probability of heads is 1 divided by 2, which is 0.5.

Correct Answer: 1/6

There is one favorable outcome out of six equally likely outcomes, giving a probability of 1/6.

Correct Answer: 1/2

The even outcomes are 2, 4, and 6, which is 3 favorable outcomes out of 6, simplifying to 1/2.

Correct Answer: P(not A) = 1 - P(A)

Since an event either occurs or does not, their probabilities sum to 1, so the probability of the complement is 1 minus the probability of the event.

Correct Answer: 0.7

Applying the complement rule, P(not A) equals 1 minus 0.3, which is 0.7.

Correct Answer: They cannot both occur at the same time

Mutually exclusive (disjoint) events have no outcomes in common, so if one occurs the other cannot. Their joint probability is zero.

Correct Answer: P(A) + P(B)

Because disjoint events share no outcomes, the probability that either occurs is simply the sum of their individual probabilities.

Correct Answer: The occurrence of one does not change the probability of the other

Independent events do not influence one another, so knowing that one occurred provides no information about the probability of the other.

Correct Answer: P(A) times P(B)

The multiplication rule for independent events states that the probability both occur equals the product of their individual probabilities.

Correct Answer: 0.25

The flips are independent, each with probability 0.5, so the probability of two heads is 0.5 times 0.5, which equals 0.25.

Correct Answer: The probability of A occurring given that B has occurred

Conditional probability measures the likelihood of A within the restricted situation where B is known to have occurred.

Correct Answer: No, removing the first card changes the probabilities for the second

Without replacement, the first draw alters the composition of the remaining deck, so the second draw's probabilities depend on the first outcome.