Gr 10 Math Ch 11: Complemantary Events

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What is the complement of a set A?

A' is the same as set A.

A' contains elements that are not in A. (correct)

A' is a subset of A.

A' contains all elements in A.

Which statement about complementary events is true?

Complementary events can have some elements in common.

Complementary events are always equal.

The union of A and A' always equals the sample space S. (correct)

The probability of an event and its complement is always 0.

What does it mean when two events are mutually exclusive?

They share some common outcomes.

They can occur at the same time.

The occurrence of one event implies the other cannot occur. (correct)

Their probabilities sum to more than 1.

What is the sum of the probabilities of an event A and its complement A'?

Equal to 1. Signup and view all the answers

In a Venn diagram representing event A and its complement A', what does the shaded region represent?

Elements belonging to A'. Signup and view all the answers

If event A has a probability of 0.3, what is the probability of its complement A'?

0.7 Signup and view all the answers

Which statement regarding the relationship between a set and its complement is true?

A and A' are mutually exclusive sets. Signup and view all the answers

If the probability of event A is 0.7, what is the probability of its complement A'?

0.3 Signup and view all the answers

What do A and A' collectively represent in a sample space S?

The entire sample space S. Signup and view all the answers

Which identity correctly reflects the relationship between the events A and A'?

Their union equals the sample space S. Signup and view all the answers

In terms of sets, how is the complement of set A denoted?

Both B and C Signup and view all the answers

When provided with a Venn diagram displaying event A and its complement A', what does the area outside of A illustrate?

The elements that are not in A. Signup and view all the answers

What does the identity $A \cap A' = \emptyset$ imply about events A and A'?

A and A' cannot occur simultaneously. Signup and view all the answers

If $P(A) = 0.4$, what can be inferred about $P(A')$?

P(A') = 0.6 Signup and view all the answers

Which statement about the union of complementary events A and A' is accurate?

It equals the sample space S. Signup and view all the answers

What does the complement of set A also represent in relation to set A?

Elements not in A. Signup and view all the answers

In terms of conditional probabilities, which of the following is true about A and A'?

P(A | A') = 0. Signup and view all the answers

What does the shaded area in a Venn diagram representing A and A' illustrate?

All elements not included in A. Signup and view all the answers

What is the implication of the identity $A imes A' = ext{some set}$?

The intersection of A and A' is empty. Signup and view all the answers

Which scenario best illustrates the sum of the probabilities of two complementary events?

If the probability of drawing a heart from a deck is 0.25, then the probability of not drawing a heart is 0.75. Signup and view all the answers

In the context of complementary events, what does $P(S)$ represent?

The total probability of all possible outcomes in the sample space. Signup and view all the answers

Which statement about the union of the sets A and A' is incorrect?

The resulting set from the union is equal to the empty set. Signup and view all the answers

What does the expression $P(A')$ signify in relation to event A?

The likelihood of event A not occurring. Signup and view all the answers

What are the implications of having complementary events A and A' in a probabilistic experiment?

Their outcomes cover all possible scenarios in the sample space. Signup and view all the answers