Probability practice · Easy

An unbiased die is rolled until two consecutive trails result in even numbered faces. The probability that exactly six trials are required to get two consecutive even numbered faces, is

A person draws a card from a pack of playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he fail the first two times is

Three dice are thrown. The probability that the same number will appear on each of them, is

A coin is tossed 4 times. The probability that at least one head turns up, is

Probability is 0.45 that a dealer will sell at least 20 television sets during a day, and the probability is 0.74 that he will sell less than 24 televisions. The probability that he will sell $20,21,22$, or 23 televisions during the day, is

If $C$ and $D$ are two events such that $C \subset D$ and $P(D) \neq 0$, then the correct statement among the following is:

From a bag containing 30 tickets numbered $1,2,3, \ldots 30,$ three tickets are selected at random without replacement. Suppose these tickets are arranged as $x_1 < x_2 < x_3$. The probability that $x_2=15$ and $x_3>20$, is

If $\mathrm{A}$ and $\mathrm{B}$ be two events such that $P(A)=\frac{3}{8}, P(B)=\frac{5}{8}$ and $P(A \cup B)=\frac{3}{4}$, then $P(A / B) \times P\left(A^{\prime} / B\right)$ is equal to

A six faced die is so biased that it is twice likely to show an even number as an odd number when thrown. If the die is thrown twice the probability that sum of the numbers is even is

Odds in favour of an event $A$ are 2 to 1 and odds in favour of $A \cup B$ are 3 to 1 . Consistent with this information the smallest and largest values for the probability of event $B$ are given by

A person draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade, the chance that he will fail in the first two draws is

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $X$ denotes the number of tosses of the coin, then the mean of $X$ is

A number $x$ is chosen from the set $A=\left\{33^n: n \in N\right\}.$ The probability that $x$ has 3 in units place, is

If two events $A$ and $B$ are such that $P\left( {{A^c}} \right) = 0.3,\;P\left( B \right) = 0.4$ and $P\left( {A \cap {B^c}} \right) = 0.5,$ then$\;P\left[ {\frac{B}{{\left( {A \cup {B^c}} \right)}}} \right]$ is equal to

A bag contains 5 red, 3 white and 2 black balls. If a ball is picked at random, the probability that it is red is

In a multiple choice question there are four alternative answers, of which one or more are correct. A candidate will get marks in the question only if he ticks all the correct answers. The candidate decides to tick answers at random. If he is allowed upto three chanes to answer the question, the probability that he will get marks in the question, is

Kiran is deciding whether to visit Russia or Ukrain for the holidays. She makes her decision by rolling a regular 6-sided die. If she gets 1 or 2 she goes to Ukrain, if she rolls a 3,4 or 5 she goes to Russia. If she rolls a 6 she rolls again, the probability that she goes to Ukrain is $p$, then $5 p$ is

Out of 40 consecutive integers, two are chosen at random, the probability that their sum is odd is

If $A\;\,\mathrm{and}\,\,B$ are arbitrary events, then

In a binomial distribution the mean is 15 and variance is 10. Then parameter $n$ is

If a die is thrown and a card is selected at random from a deck of 52 playing cards, then the probability of getting an even number on the die and a spade card is

One Indian and four American men and their wifes are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is

If the range of a random variable $X$ is {0,1,2,3,4,…} with $P\left( {X = k} \right) = \frac{{\left( {k + 1} \right)a}}{{{3^k}}}$ for $k \ge 0,$ then $a$ is equal to

Probability of all 3 digit numbers having all the digits same is

For two events $A$ and $B$, if $P\left( A \right) = P\left( {\frac{A}{B}} \right) = \frac{1}{4}$ and $P\left( {\frac{B}{A}} \right) = \frac{1}{2},$ then

A random variable X takes values $-1,0,1,2$ with probabilities $\frac{1+3 p}{4}, \frac{1-p}{4}, \frac{1+2 p}{4}, \frac{1-4 p}{4}$ respectively, where $p$ varies over $R$. Then the minimum and maximum values of the mean of $X$ are respectively

Two integers $x$ and $y$ are chosen with replacement out of the set $\{0,1,2,3, \ldots, 10\}.$ Then the probability that $|x-y|>5,$ is

A die is tossed thrice. A success is getting 1 or 6 on a toss. The mean and the variance of number of successes

A coin is tossed three times. The probability of getting head and tail alternatively, is