Question

Practice.
1. There are N men and M women in a group. Two random persons are selected. Calculate the
probabilities:
a) a man and a woman are selected;
b) two men are selected;
c) two women are selected.
2. If necessary, correct the mistakes in formulas:
a) ?(∅) = 1;
b) ?(? ∪ ?) = ?(?) ∙ ?(?), if ? ∩ ? ≠ ∅.
c) If ? ⊂ ?, then ?(?) > ?(?),
d) ?(Ω) = 1.

Theory. Explain what probability is, formula of classical probability. List properties of probability.

Answer 1

1. There are N men and M women in a group.

a) P ( a man and a woman) =( ^NC₁.  ^MC₁)/ ^N+MC₂

b) P ( Two men ) = ^NC₂/ ^N+MC₂

c) P( Two women ) = ^MC₂ /  ^N+MC₂

2. a) FALSE, P( ) =0

b)FALSE ,   P ( A u B) = P(A) + P(B) if A n B=

c) FALSE, If A c B then P( A) < P(B)

d) TRUE, P( )=1

3. Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

  The probability of a simple event happening is the number of times the event can happen, divided by the number of possible events, the formula is P(A) = f / N. P(A) means “probability of event A” (event A is whatever event you are looking for, like winning the lottery).
“f” is the frequency, or number of possible times the event could happen.
N is the number of times the event could happen.

LIST OF PROPERTIES OF PROBABILITY-

1.The sum of the probabilities of an event and its complementary is 1, so the probability of the complementary event is:

2.The probability of an impossible event is zero.

3 The probability of the union of two events is the sum of their probabilities minus the probability of their intersection.

4. If an event is a subset of another event, its probability is less than or equal to it.

5. If A₁, A₂, ..., A_k are mutually exclusive between them, then:

6. If the sample space S is finite and an event is S = {x₁, x₂, ..., x_n} then: