Probability Test

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Probability Test - 3

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Question 1
1 / -0.25

The conditional probability of an event E, given the occurrence of the event F is given by

A

B

C

D

Solution

The conditional probability of an event E, given the occurrence of the event F is given by :
Question 2
1 / -0.25

A coin is tossed three times, if E : head on third toss , F : heads on first two tosses. Find P(E|F)

A
2/3

B
1/3

C
1/2

D
1/5

Solution

S ={HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}
E = {HHH,HTH,THH,TTH}
F = {HHH,HHT}
E ∩F = {HHH}
Question 3
1 / -0.25

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

A
27/102

B
29/102

C
25/102

D
23/102

Solution

Required probability : P(BB) = P(B) X P(B/B) ……………{B means black card}
Question 4
1 / -0.25

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

A
22/133

B
23/133

C
27/133

D
25/133

Solution

Let
E₁ and E₂ are events that a person has disease and the person has not disease.
Let A = event that the test result is positive
Question 5
1 / -0.25

Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is

A
41/133

B
3/13

C
1/13

D
2/13

Solution

The possible values of X are 0 , 1 and 2 .
As we know that pack of cards contains 4 aces.

Therefore , the probability distribution of X is :

Therefore required value of
E(X) is = 0+ 384/2652 + 24/2652 = 408/2652 = 2/13.
Question 6
1 / -0.25

The conditional probability of an event E, given the occurrence of the event F

A
0 < P (E|F) < 1

B
0 ≤P (E|F) ≤1

C
0 ≤P (E|F) <1

D
0 < P (E|F) ≤ 1

Solution

As the probability of any event always lies between 0 and 1. Therefore , 0 ≤P (E|F) ≤1.
Question 7
1 / -0.25

A coin is tossed three times, if E : at least two heads , F : at most two heads. Find P(E|F)

A
2/5

B
3/7

C
2/3

D
2/7

Solution
Question 8
1 / -0.25

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.

A
47/91

B
49/91

C
4191

D
44/91

Solution

Total oranges = 15., Good Oranges = 12. Let G stands for a good orange. Therefore , Required Probability = P(GGG) = P(G).P(G/G).P(G/GG)
Question 9
1 / -0.25

There are three coins. One is a two headed coin (having head on both faces),another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?

A
4/9

B
2/9

C
1/9

D
5/9

Solution

Let
E₁ , E₂ and E₃ and are events of selection of a two headed coin , biased coin and unbiased coin respectively.
Let A = event of getting head.
Question 10
1 / -0.25

Which of the following conditions do Bernoulli trials satisfy?

A
finite number of dependent trials

B
infinite number of dependent trials.

C
infinite number of independent trials

D
finite number of independent trials

Solution

Bernoulli trials satisfies the finite number of independent trials .