AP EAPCET (Engineering) Probability — practice questions
114 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Probability in the app →A fair coin is tossed twice. How many outcomes are there in the sample space?A fair six-sided die is rolled once. What is the probability of getting an even number?Events $A$ and $B$ are mutually exclusive with $P(A) = 0.4$ and $P(B) = 0.3$. Find $P(A \cup B)$.A **random variable** is best defined as:A **discrete** random variable is one whose possible values:For a continuous random variable $X$, the probability that $X$ equals any specific value is:The **cumulative distribution function (c.d.f.)** $F(x)$ of a discrete random variable is:When two fair dice are rolled and $X$ denotes the sum of the upper faces, the range of $X$ is:If a fair coin is tossed twice and $X$ = number of heads, then $P[X = 1]$ equals:If two cards are drawn with replacement from a deck of 52, $P[X = 2]$ where $X$ = number of aces equals:A fair die is thrown. Let $X$ = number of factors of the number on the upper face. $P[X = 2]$ equals:$f(x) = 3x^2$ for $0 < x < 1$ is the p.d.f. of $X$. The probability $P[1/2 < X < 1]$ is:If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:For p.d.f. $f(x) = x/8$, $0 < x < 4$, the probability $P[x < 1.5]$ is:Find $k$ if $f(x) = kx$ for $0 < x < 2$ and 0 otherwise is a valid p.d.f.The c.d.f. $F(x)$ of the p.d.f. $f(x) = 3x^2$ for $0 < x < 1$ is:Two cards are drawn with replacement. $X$ = number of aces. The probability $P[X \geq 1]$ equals:For p.d.f. $f(x) = x^2/3$ for $-1 < x < 2$, the probability $P[0 < X \leq 1]$ equals:For p.d.f. $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ (and 0 elsewhere), the value of $k$ is:For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:If a fair coin is tossed $n$ times, the probability of any exact pattern (like all heads) is:If a die is thrown and 'getting an odd number' is success, then $p$ and $q$ are:A bag has balls marked 0–9. Four balls drawn with replacement. Probability that **none** is marked '0' is:Probability of bomb hitting target = 0.8. Out of 10 bombs dropped, probability that **exactly 2 miss** equals The arithmetic mean of n values x1, x2, ..., xn is:Median of an odd-length sorted data set is:Probability of a certain event:Probability of rolling a 6 on a fair die:For independent events A and B, P(A and B) equals:For mutually exclusive events A and B, P(A or B) equals:Find mean of {2, 4, 6, 8, 10}:Mode of {1, 2, 2, 3, 4, 4, 4, 5}:Variance of {2, 4, 6, 8, 10}:Standard deviation of {2, 4, 6, 8, 10}:P(at least one head in 2 fair coin tosses):Probability of drawing a heart from a standard 52-card deck:P(drawing an Ace OR King from a deck) =Two dice rolled. P(sum = 7) =Bayes' theorem relates P(A|B) and P(B|A):Number of ways to arrange 5 distinct books on a shelf:Number of ways to choose 3 students from a class of 10:A box has 5 red, 3 blue marbles. Probability of drawing 2 red and 1 blue in any order (without replacement, 3 For a Poisson distribution with mean λ = 3, P(X = 2):Standard deviation has the same units as:For 50 students with mean score 60 and variance 25, the coefficient of variation (sigma/mean × 100%):P(picking a king OR a heart from 52 cards):Two events A and B: P(A) = 0.3, P(B) = 0.4, P(A and B) = 0.1. Are they independent?5 cards drawn from a standard deck. Probability all 5 are aces:Number of distinguishable arrangements of letters in 'STATISTICS':Conditional probability P(A | B) is defined as:In a survey, 60% read newspaper A, 40% read B, 20% read both. P(reading neither):Binomial distribution: P(X = k) for n trials, success probability p:E(X) and Var(X) for fair coin tossed n times (success = heads, p = 0.5):Two cards drawn from a deck (no replacement). P(both kings):For events E and F with P(F) > 0, P(E|F) is which ratio?Three fair coins are tossed. Given the first shows tail, find P(at least two heads).If P(B) = 9/13 and P(A ∩ B) = 4/13, what is P(A|B)?For an event F with P(F) > 0 in sample space S, P(S|F) equals what?If P(E|F) = 0.35, what is P(E'|F)?If P(F) = 0.4 and P(E|F) = 0.5, find P(E ∩ F).Events E and F, both with nonzero probability, are independent ifE and F are independent, P(E) = 0.3 and P(F) = 0.5. Find P(E ∩ F).A card is drawn from 52. Given it is a spade, P(it is an ace)?A partition of a sample space must have events that areFor a nonempty event E, which pair always forms a partition of S?How many partitions can a given sample space have?E1, E2 partition S: P(E1)=0.6, P(A|E1)=0.2, P(E2)=0.4, P(A|E2)=0.5. Find P(A).Bag I: 3 red, 4 black; Bag II: 5 red, 6 black. Pick a bag at random; P(red)?When Bayes' theorem is applied, the events E1, ..., En are calledIn Bayes' theorem, P(Ei) before observing A is called theBayes' theorem is also called the formula for the probability of what?What problem did John Bayes solve using conditional probability?In which year was Bayes' theorem published posthumously?Whose 1654 correspondence laid the first foundation of probability science?Three dice are thrown. Which total is more likely, 9 or 10?Who discovered the binomial distribution?Which Dutch scientist wrote the first book on probability after Pascal and Fermat?Which Russian mathematician formulated the axiomatic approach to probability?The event E ∩ F is also written in which short form?The event E ∩ F describes which situation?Once F is known to have occurred, E is judged within which sample space?A family has two children. Given at least one is a boy, P(both boys)?Two dice are thrown. Given doubles, P(the sum is 8)?Two dice are thrown. Given the first shows 5, P(sum is at least 10)?One ace is drawn from a deck and kept aside. P(the next card is an ace)?A fair coin is tossed twice. Given the first is tails, P(second is heads)?P(A) = 0.6, P(B) = 0.5, P(A ∩ B) = 0.3. Find P(A|B).Two archers hit with chances 0.7 and 0.8 independently. P(at least one hits)?A fair coin is tossed 3 times. P(at least one head)?1% are ill; test is + for 90% of ill, 5% of healthy. P(ill | +)?Machine A makes 60% of items (2% faulty), B makes 40% (5% faulty). P(faulty)?Bag I: 2 white, 3 red; Bag II: 4 white, 5 red. A bag is chosen at random. P(white)?Bag I: 2 white, 3 red; Bag II: 4 white, 5 red. A white ball is drawn. P(Bag II)?If P(E ∩ F) = 0.12 and P(F) = 0.4, find P(E|F).In Bayes' theorem, the denominator sum of P(Ej)P(A|Ej) equalsTwo events are independent when one occurringTwo cards are drawn without replacement. P(a king, then a queen)?In probability, the empty set is the event calledWhen a die is thrown, getting a multiple of 7 isA sample space has n distinct elements. How many simple events does it have?How many simple events arise when two coins are tossed together?Three coins are tossed. How many sample points favour exactly one head?The complementary event 'not A' of an event A in a sample space S isFor events A and B, the union A U B stands for the eventThe event 'A but not B' corresponds to the setEvents 'odd number' and 'even number' on one die areTwo events are mutually exclusive when theyEvents E1, E2, ..., En are exhaustive when their union isOn a die, the events 'less than 4', 'a 3 or 4' and 'greater than 4' areTwo dice: events 'sum even' and 'sum multiple of 3' share how many outcomes?In three coin tosses, 'no head', 'exactly one head' and 'at least two heads' areThe domain of the probability function P is theA coin has P(H) = 1/4. For a valid assignment, P(T) must beIf P(A) = 0.6 and P(B) = 0.7, the smallest possible P(A and B) is