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Question2
a).A balanced coin is tossed three times. Calculate the probability that exactly two of the three tosses result in heads.
b). A coin is tossed and a single 6-sided die is rolled. Find the probability of getting a head on the coin anda 4 on the die?
c). Prove that the following events are independent or dependents
i) Tossing a pair of fair dice and two events A & B are defined as Sum equal to 3 and 6 respectively
ii) Toss a pair of fair dice with defining two events A and B as both red and green die show 2
iii) Toss a fair coin twice with defining two events A and Bas A: head on second toss
and B: head on first toss
d). Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then
one card is drawn randomly. If it is known that the number on the drawn card is
more than 3, what is the probability that it is an even number?
Question1
b) The English alphabet contains 21 consonants and 5 vowels. How many strings of
six lower case letters of the English alphabet contain:i) Exactly one vowel?
i) Exactly 2 vowels
III) At least 1 vowel
IV) At least 2 vowels)
c).If A and B are independent events, show that A and B are also independent. Are A And B independent?
d) Find Population Mean, median, mode and Sample Standard Deviation for the following
data set: 5, 10, 15, 20, 25, 30
Q2
if two events, A and B, are such that P(A) = .5, P(B) = .3, and P(A intersection B) = .1, findthe following:
a).P(A|B)
b). P(B|A)
c).P(A|AUB)
d).P(A|A intersection B)
e). P(A intersection B|A U B)
Consider the following events n the toss of a single die: A: Observe an odd numbers,B: Observe an even numbers, C: Observe a I or 2.
a). Are A and B independent events?
b). Are A and C independent events?
Q3
Cards are dealt, one at a time, from a standard 52-card deck.
a). if the first 2 cards are both spades, what is the probability that the next 3 cards are alsospades?
b). If the first 3 cards are all spades, wlhat is the probability that the next 2 carcds are alsospades?
C).It the tirst 4 cards are all spades, what 1s the probability that the next card is also aspade?
Q4
Can A andB be mutually exchusive if P(A) 4 and P(B)=.7? If P(A) = .4 and P(B) .3=Why?
Q
Two events A and B are such that P(A) =2. P(B) =.3, aud P(A U B) =4. Find the following:
a. P(A intersection B)
b. P(A' U B')
c. P(A' intersection B')
d. P(A' |B)
A monkey Is to demonstrate that she recoginizes colors by tossing one red, one black,and one white ball into boxes of the same respective colors, one ball to a boOx. If themonkey las not leamed the colorS and nerely tosses one ball into each box al random,find the probabilities of the following results:
a. There are no color matches.
b.There i5 exactly one color match.
Q7
Suppose that two balanced dice are tossed repeatedly and the sum of the twouppermost faces is determined on cach toss. What is the probability that we obtana
.a) sum of 3 before we obtaim a sum of 7?
b). sum of 4 before we obtain a sum of 7?
Q8
Males and females are observed to react differently to a given set of circumstances. Ithas been observed that 70% of the females react positively to these circumstances,whereas only 40o of males react positively. A group of 20 people, 15 female and 5male, was subjected to these cireumstances, and the subjects were asked to describetheir reactions on a wIitten questionaire. A respouse picked at random fiom the 20was negative. What is the probability that it was that of a male?
