Question

Understand and apply rules of permutations and combinations, additive and multiplicative laws and conditional probability to evaluate probabilities of events. (a) Translate the following events into equations including the events A, B and C as well as operations of complementation, union and intersection. Also draw the corresponding Venn diagram. i) at most one of the events A, B, C occurs ii) all three events A, B and C occurs iii) either event A occurs or, if not, then B also does not occur. (b) One male student and one female student from BEE-4C choose at random a number in the interval [0, 2]. We assume a uniform probability law under which the probability of an event is proportional to its area. Consider the following events: A: The magnitude of the difference of the two numbers is greater than 1/3. B: At least one of the numbers is greater than 1/3. C: The two numbers are equal. D: Alice's number is greater than 1/3. Find the probabilities $P(B)$, $P(C)$, and $P(A cap D)$. (c) A joker in lucky irani circus is trying walk on an tight rope. The joker is, in the middle of a really long tightrope, and manages to keep his balance, but takes a step forward with probability p and takes a step back with probability (1-p). (i) What is the probability that after two steps the joker will be at the same place on the rope? (ii) What is the probability that after three steps, the joker will be one step forward from where he began? (iii) Given that after three steps he has managed to move ahead one step, what is the probability that the first step he took was a step forward?

          Understand and apply rules of permutations and combinations, additive and multiplicative laws
and conditional probability to evaluate probabilities of events.
(a) Translate the following events into equations including the events A, B and C as well as operations
of complementation, union and intersection. Also draw the corresponding Venn diagram.
i)
at most one of the events A, B, C occurs
ii)
all three events A, B and C occurs
iii)
either event A occurs or, if not, then B also does not occur.
(b) One male student and one female student from BEE-4C choose at random a number in the interval
[0, 2]. We assume a uniform probability law under which the probability of an event is proportional to
its area. Consider the following events:
A: The magnitude of the difference of the two numbers is greater than 1/3.
B: At least one of the numbers is greater than 1/3.
C: The two numbers are equal.
D: Alice's number is greater than 1/3.
Find the probabilities $P(B)$, $P(C)$, and $P(A cap D)$.
(c) A joker in lucky irani circus is trying walk on an tight rope. The joker is, in the middle of a really
long tightrope, and manages to keep his balance, but takes a step forward with probability p and takes a
step back with probability (1-p).
(i) What is the probability that after two steps the joker will be at the same place on the rope?
(ii) What is the probability that after three steps, the joker will be one step forward from where he began?
(iii) Given that after three steps he has managed to move ahead one step, what is the probability that the
first step he took was a step forward?

Understand and apply rules of permutations and combinations, additive and multiplicative laws
and conditional probability to evaluate probabilities of events.
(a) Translate the following events into equations including the events A, B and C as well as operations
of complementation, union and intersection. Also draw the corresponding Venn diagram.
i)
at most one of the events A, B, C occurs
ii)
all three events A, B and C occurs
iii)
either event A occurs or, if not, then B also does not occur.
(b) One male student and one female student from BEE-4C choose at random a number in the interval
[0, 2]. We assume a uniform probability law under which the probability of an event is proportional to
its area. Consider the following events:
A: The magnitude of the difference of the two numbers is greater than 1/3.
B: At least one of the numbers is greater than 1/3.
C: The two numbers are equal.
D: Alice's number is greater than 1/3.
Find the probabilities P(B), P(C), and P(A cap D).
(c) A joker in lucky irani circus is trying walk on an tight rope. The joker is, in the middle of a really
long tightrope, and manages to keep his balance, but takes a step forward with probability p and takes a
step back with probability (1-p).
(i) What is the probability that after two steps the joker will be at the same place on the rope?
(ii) What is the probability that after three steps, the joker will be one step forward from where he began?
(iii) Given that after three steps he has managed to move ahead one step, what is the probability that the
first step he took was a step forward?

Added by Melissa K.

Question

Please give Ace some feedback