Probability practice · Easy

A fair coin is tossed 100 times. The probability of getting tails an odd number of times, is

Three faces of a fair dice are yellow, two faces red and one blue. The dice is tossed three times. The probability that the colours, yellow, red and blue appear in the first, second and third tosses respectively is

Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has atleast one girl is

Three identical dice are rolled. The probability that same number appears on them, is

If $A$ and $B$ are two subsets of set $X=\{1,2,3,4,5\}$, then the probability that $A \cap B$ contains just two elements is

Let Ajay will not appear in JEE exam with probability $p=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $q=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is

The chances to fail in physics are 20% and the chances to fail in mathematics are 10%. What are the chances to fail in at least one object?

In a three throw of two dice, the probability throwing doublets not more than twice is

Let $A$ and $B$ are two events and $P\left( {A'} \right) = 0.3,\;P\left( B \right) = 0.4,\;P\left( {A \cap B'} \right) = 0.5,$ then $P\left( {A \cup B'} \right)$ is

If $p$ and $q$ are chosen from the set $\{1,2,3$, $4,5,6,7,8,9,10\}$, with replacement, the probability that the roots of the equation $x^2+2 p x+q=0$ are real is

Let $0 < P(A) < 1,0 < P(B) < 1$ and $P(A \cup B)=P(A)+P(B)-P(A) P(B)$. Then,

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

A fair coin is tossed $n$ times. If the probability that heads occurs 6 times is equal to the probability that heads occurs 8 times, then value of $n$ is

For two events $A$ and $B$ it is given that $P(A)=P(A / B)=\frac{1}{4}$ and $P(B / A)=\frac{1}{2}$. Then,

A bag contains 7 red and 2 white balls and another bag contains 5 red and 4 white balls. Two balls are drawn, one from each bag. The probability that both the balls are white, is

If $P\left( A \right) = P\left( B \right) = x\;$ and $P\left( {A \cap B} \right) = P\left( {A' \cap B'} \right) = \frac{1}{3}$, then $x$ is equal to

If $P(A)=0.4, P(B)=0.8$ and $P(B / A)=0.6$, then $P(A \cup B)$ is equal to

Four persons can hit a target correctly with probabilities $\frac{1}{2},\,\frac{1}{3},\,\frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

If the probability of hitting a target by a shooter in any shot, is $\frac{1}{3}$, then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than $\frac{5}{6}$, is

Three natural numbers are taken at random one by one with replacement from the set $\mathrm{A}=\{x \mid 1 \leq x \leq 100, x \in N\}$. The probability that the $\mathrm{AM}$ of the number is 25 is

In a school 80 students like chocolate, 40 like coffee if the number of students doesn't like any of them is equal to the number of students who like both of them then what is the total number of students in the school?

In a game called "odd man out" each person in a group of $n \geq 2$ persons tosses a coin to determine who will buy refreshment for the entire group. The odd man out is the one whose outcome is different from the rest of the persons. The probability that there is a loser in the game is

If $A$ and $B$ are any two events, then $P\left( {A \cap B'} \right)$ is equal to

The Probability of solving a problem by three students $A, B, C$ is $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ respectively. The probability that the problem will be solved is

For a random variable $X,E\left( X \right) = 3$ and $E\left( {{X^2}} \right) = 11.$ Then, variable of $X$ is

The event $A$ is independent of itself if and only if $P(A)$ is

Let $A$ and $B$ be two events such that $P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4}$ and $P(\bar{A})=\frac{1}{4}$, where $\bar{A}$ stands for the complement of the event $A$. Then the events $A$ and $B$ are

If X follows a binomial distribution with parameters $n=8$ and $p=1 / 2$, then $P(|X-4| \leq 2)$ equals

Three letters are written to different persons and addresses to three envelops are also written. Without looking at the addresses, the probability that the letters go into right envelops is

If random variable $X$ has the following probability distribution:
$\begin{array}{cccccccccccccccccccc} X&:&0&1&2&3&4&5&6&7&8 \\ {P(X = x)}&:&a&{3a}&{5a}&{7a}&{9a}&{11a}&{13a}&{15a}&{17a} \end{array}$
then the value of $a$ is