#Q1. Two events ?1 and ?2 are defined on the same probability space such that: ?(?1...
#Q1. Two events ?1 and ?2 are defined on the same probability space such that: ?(?1 ) = 0.7 , ?(?2 ) = 0.5 , and ?(?1 ??? ?2 ) = 0.3.
a) Find ?(?1 ?? ?2 ).
b) Find ?(?1 | ?2 ).
c) Are ?1 and ?2 mutually exclusive (disjoint)? and why?
d) Are ?1 and ?2 independent? and why?
#Q2. A bookshelf in a library contains 5 Math books and 15 books of other subjects. If we randomly select two books one after another and without replacement, find the probability of getting 2 math books.
Homework Answers
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#Q1. Two events ?1 and ?2 are defined on the same probability
space such that: ?(?1...
(7) The events A and B are mutually exclusive (disjoint). If P(A) = 0.7 and P(B)...
(7) The events A and B are mutually exclusive (disjoint). If P(A) = 0.7 and P(B) = 0.2, what is P(A or B)? A) 0.14 B) 0 C) 0.9 D) 0.5 (8) The events A and B are mutually exclusive (disjoint). If P(A) = 0.2 and P(B) = 0.1, what is P(A and B)? A) 0.02 B) 0 C) 0.5 D) 0.3 (9) A probability experiment is conducted in which the sample space of the experiment is S = {1,...
1) What does it mean for events to be mutually exclusive? Give an example of events...
1) What does it mean for events to be mutually exclusive? Give an example of events that are mutually exclusive and an example of events that are not. 2) How is the probability of an event found? 3) When drawing one card at random from a standard deck of cards, what is probability of getting a king, P(K)? Now let's put a condition on that probability, find the probability of getting a king given that the card is a face...
Needing help with these two questions please. 4.20 A and B are events defined on a...
Needing help with these two questions please.
4.20 A and B are events defined on a sample space, with P(A) 0.7 and P(B | A) 0.4. Find P(A and B) 4.21 A and B are events defined on a sample space, with P(A) 0.6 and P(A and B) = 0.3. Find P(B | A).
Q1) Consider two events P and Q. a. Write the general formula used to calculate the probability that either event P occu...
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
All of these questions are about a normal deck of 52 cards 1. Suppose two cards...
All of these questions are about a normal deck of 52 cards 1. Suppose two cards are chosen without replacement. If we consider only the suits of the two cards, what is the sample space? 2. Suppose a single card is drawn. If we define events ? and ? as below, find ?(? or ?). ? = card is a spade ? = card is a king 3. Suppose again a single card is drawn from the deck. Define two...
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB)...
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB) -0.3 and PLAUB)=0.8. Calculate: 1) P(AB): ii) P(BA): iii) PIBIA B): be independent of A and such that B and Care Let the event C in mutually exclusive. Calculate: iv) P(AC); v) PIANBNC). (8 Marks)
1. Events A and B are defined on a sample space S such that P((A ∪...
1. Events A and B are defined on a sample space S such that P((A ∪ B) C) = 0.5 and P(A ∩ B) = 0.2.If P(A) = 0.3, what does P((A ∩ B) | (A ∪ B) C) equal?
(1) Name the four properties of probability: (2) Another word for mutually exclusive: (3) A sample...
(1) Name the four properties of probability: (2) Another word for mutually exclusive: (3) A sample space contains all possible . (4) Grine an example of independent events - (5) Gire an example of equally likely outcomes. (6) Write down the sample space for all families of 2 children: s={ (7) Complete the tree PAB) PCBIB PLAE rite down the corresponding probability table to the r ear and a ban. Sum= — PRAB) (9) Independence and are Word (10) Towo...
A certain illness has two symptoms associated with it - a fever and fatigue. There is...
A certain illness has two symptoms associated with it - a fever and fatigue. There is a 90% probability that at least one of the two symptoms occurs for a randomly selected person with the illness. There is an 80% probability that a randomly selected person with the illness will come down with a fever and there is a 50% probability that a randomly selected person with the illness will feel fatigued. Please answer the following three questions: 1) Are...
QUESTION If A and 8 are two mutually exclusive events and P(A) -0.5 and P(B) -0.3,...
QUESTION If A and 8 are two mutually exclusive events and P(A) -0.5 and P(B) -0.3, then the probability of joint event AU 8 should be QUESTION 2 Does the following Venn Diagram correctly describe the event (AUB)nC O True False
Needing help with these two questions please.
4.20 A and B are events defined on a sample space, with P(A) 0.7 and P(B | A) 0.4. Find P(A and B) 4.21 A and B are events defined on a sample space, with P(A) 0.6 and P(A and B) = 0.3. Find P(B | A).
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB) -0.3 and PLAUB)=0.8. Calculate: 1) P(AB): ii) P(BA): iii) PIBIA B): be independent of A and such that B and Care Let the event C in mutually exclusive. Calculate: iv) P(AC); v) PIANBNC). (8 Marks)
(1) Name the four properties of probability: (2) Another word for mutually exclusive: (3) A sample space contains all possible . (4) Grine an example of independent events - (5) Gire an example of equally likely outcomes. (6) Write down the sample space for all families of 2 children: s={ (7) Complete the tree PAB) PCBIB PLAE rite down the corresponding probability table to the r ear and a ban. Sum= — PRAB) (9) Independence and are Word (10) Towo...
QUESTION If A and 8 are two mutually exclusive events and P(A) -0.5 and P(B) -0.3, then the probability of joint event AU 8 should be QUESTION 2 Does the following Venn Diagram correctly describe the event (AUB)nC O True False
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