Probability practice · Mixed difficulty

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

From a group of 8 boys and 3 girls, a committee of 5 members to be formed. Find the probability that 2 particular girls are included in the committee

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

In a sequence of independent trials, the probability of success is $1 / 4$. If $p$ denotes the probability that the second success occurs on the fourth trial or later trial, then $32 p-20$ 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

A bag contains some white and some
black balls, all combinations of balls being equally likely. The
total number of balls in the bag is 10. If three balls are drawn
at random without replacement and all of them are found to
be black, the probabili ty that the bag contains 1 white and
9 black balls is

A complete cycle of a traffic light takes 60 s. During each cycle the light is green for 25 s, yellow for 5 s and red for 30 s. At a randomly chosen time, the probability that the light will not be green, is

An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success

There are 10 pairs of shoes in a cupboard, from which 4 shoes are picked at random. If $p$ is the probability that there is at least one pair, then $323 p$ -97 is equal to

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 $A$ and $B$ are events such that $P(A)=0.42, P(B)=0.48$ and $P(A \text{ and } B)=0.16$, then,

I. ${P}(\operatorname{not}{A})=0.58$

II. ${P}(\text{not }{B})=0.52$

III. ${P}({A} \text{ or }{B})=0.47$

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

Seven chits are numbered 1 to 7. Four chits are drawn one by one with replacement. The probability that the least number appearing on any selected chit is 5, 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

Let $M$ be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space $S=\left\{x \in \mathbb{Z}: x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A=\{x \in S: x$ is a multiple of 3$\}$. Then $P(A)$ is equal to

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