Question

1.Pick two real numbers a, b uniformly at random from infinite sample space [-1,1]. What is the probability that a2+b2>1?
π/4
1−π/4
π/16
1−π/16


2.Which of the following is true for two events A and B each having non-zero probability of occurrence? If A and B are mutually exclusive, then they are also independent. If A and B are independent, then they can be mutually exclusive.
Only 1.
Only 2.
Both 1 and 2.
Neither 1 nor 2.

3.Suppose the Covid-19 RT-PCR test is 95% accurate. Also assume the prevalence of Covid is 0.2, i.e. 20% of the population is Covid infected. If your RT-PCR test comes out positive, what is the probability that you are infected? 19/20
19/23
17/20
17/23

4.Suppose you roll a dice twice. What is the probability that the sum of two rolls is an even number given that the first roll was an even number.
1
0
1/2
2/3



pls answer all these question ...​

Answer 1

Answer: Q. 1

1 - π/4

Q2. Neither

Q3. 19/23

Q4 1/2

Step-by-step explanation:

Q1 The possible points can be represented by a a graph with a on x axis and b on y axis. All the possible points lie in the square of 4 units.

a2 + b2 = 1 is the eq of a circle. Anything outside this is greater than one. The sample space will be the square and the area we want is between the circle and the square.

So, (4 - π/4)/4

= 1 - π/4

Q3 Using Bayes Theorem. Example in attachment.

Q4 Using Sample Space

Answer 2

4. Answer : 1/2
Since it is given first roll is even.
Second roll must also be even. so that the overall sum will be even I.e., even + even = even
P(second even I.e., 2,4,6)= 3/6 = 1/2