Probability practice · Easy

If any four numbers are selected and they are multiplied, then the probability that the last digit will 1, 3, 5 or 7, is

Let $U_1$ and $U_2$ be two urns such that $U_1$ contains 3 white and 2 red balls, and $U_2$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $u r n U_1$ and put into $U_2 \cdot$ However, if tail appears then 2 balls are drawn at random from $U_1$ and put into $U_2$. Now, 1 ball is dravn at randnm from $U_2$. Then the probability of the drawn ball from $U_2$ being white is

A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads, is

Let $X$ be a set containing 10 elements and $P(X)$ be its power set. If $A$ and $B$ are picked up at random from $P(X)$, with replacement, then the probability that $A$ and $B$ have equal number elements, is :

Let ${S}$ be a sample space containing outcomes $\omega_1, \omega_2, \omega_3, \ldots, \omega_{{n}}$ i.e., ${S}=\left\{\omega_1, \omega_2, \ldots ., \omega_{{n}}\right\}$.

Then, which of the following is true?

I. $0 \leq {P}\left(\omega_{{i}}\right) \leq 1$ for each $\omega_{{i}} \in {S}$

II. ${P}\left(\omega_1\right)+{P}\left(\omega_2\right)+\ldots . {P}\left(\omega_{{n}}\right)=1$

III. For any event ${A}, {P}({A})=\sum {P}\left(\omega_{{i}}\right), \omega_{{i}} \in{A}$

Ten unbiased coins are thrown simultaneously. The probability of getting at least seven heads is

10 different vectors are lying on a plane out of which four are parallel with respect to each other. Probability that three vectors chosen from them will satisfy the equation $\lambda_1 \mathbf{a}+\lambda_2 \mathbf{b}+\lambda_3 \mathbf{c}=0$, where $\lambda_1, \lambda_2$ and $\lambda_3 \neq 0$ is

If $m$ is a natural such that $m \leq 5$, then the probability that the quadratic equation $x^2+m x+\frac{1}{2}+\frac{m}{2}=0$ has real roots is

In a certain town, $40 \%$ of the people have brown hair, $25 \%$ have brown eyes and $15 \%$ have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes is

A problem in Mathematics is given to three students $A, B, C$ and their respective probability of solving the problem are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$. Probability that the problem is solved, is

Bag $A$ contains 7 white balls and 3 red balls. Bag $B$ contains 3 white balls and 2 red balls. A ball is chosen randomly and found to be red then find the probability that it is taken from bag $A$.

The probability that an event $A$ happens in one trial of an experiment is 0.4. Three independent trials of the experiment are formed. The probability that the event A happens at least once is

A bag contains $(n+1)$ coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is 7/12, then the value of $n$ is

A card is drawn at random from a pack of 52 cards. The probability that the drawn card is a court card i.e. a jack, a queen or a king, is

If the probability of $\mathrm{A}$ to pass in an examination is 0.3 and for $\mathrm{B}$ is 0.5 . Then the probability that either A or B pass in the examination is

If $X$ follows a binomial distribution with parameters $n = 100$ and $P = \frac{1}{3}$, then $P\left( {X = r} \right)$ is maximum when $r$ is equal to

A die is thrown twice and the sum of the numbers appearing is observed to be 6 . The conditional probability that the number 4 has appeared at least once, is

Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is 6?

A coin is tossed $n$ times the probability of getting head at least once is greater than 0.8. Then the least value of such $n$ is

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event.

Given below are two statements:

(S1) : If $P(A)=0$, then $A=\varnothing$

(S2) : If $P(A)=1$, then $A=\Omega$

Then

A bag contains 4 tickets numbered 1, 2, 3, 4 and another bag contains 6 tickets numbered 2, 4, 6, 7, 8, 9. One bag is chosen and a ticket is drawn. The probability that the ticket bears the number 4 is

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$, then $P(A / \bar{B})=$

$A$ and $B$ are two events such that odds against $A$ are $2: 1$ odds in favour of $A \cup B$ are $3: 1$. If $x \leq P(B) \leq y$, then the ordered pair $(x, y)$ is

A coin is tossed $2 n$ times. The chance that the number of times one gets head is not equal to the number of times one gets tail, is

$A$ is a set containing $n$ elements. A subset $P$ of $A$ is chosen at random. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ is again chosen at random. The probability that $P$ and $Q$ have equal number of elements, is

A company has two plants A and B to manufacture motorcycles. $60 \%$ motorcycles are manufactured at plant A and the remaining are manufactured at plant B. $80 \%$ of the motorcycles manufactured at plant A are rated of the standard quality, while $90 \%$ of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If p is the probability that it was manufactured at plant B, then $126 \mathrm{p}$ is

It is $8: 5$ against a person who is now 40 years old living till he is 70 and $4: 3$ against a person now 50 living till he is 80 . The probability that at least one of these persons will be alive 30 years hence, is

Three coins are tossed together, then the probability of getting at least one head is

Out of $3 n$ consecutive integers, three are selected at random. Find the probability that their sum is divisible by 3 , is

Two events $A$ and $B$ are such that $P(B)=0.55$ and $P\left(A B^{\prime}\right)=0.15$. The probability of occurrence of at least one of event is