Probability practice · Mixed difficulty

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

The probability of getting a total of at least 6 in the simultaneously throw of three dice is

A and B throw a die alternatively. If A starts throwing then the probability that he throws 5 before B throws 3 or 6 is

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

Probability that Ajay will not go to office is $\frac{1}{5}$ and probability that Ajay and Vijay will go to office is $\frac{2}{7}$, if their visits to office is independent of each other then find probability that Ajay will go to the office but Vijay will not go, is

Three people each flip two fair coins. The probability that exactly two of the people flipped one head and one tail, is

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

Of a total of 600 bolts, 20% are too large and 10% are too small. The remainder are considered to be suitable. If a bolt is selected at random, the probability that it will be suitable 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 ${A}, {P}({A})=\sum {P}\left(\omega_{{i}}\right), \omega_{{i}} \in{A}$

A sample of a 4 times is drawn at a random without replacement from a lot of 10 items containing 3 defectives. If $x$ denotes the number of defective items in the sample, then $P(0 < x < 3)$ is equal to

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

A five digit number if formed by writing the digits 1, 2, 3, 4, 5 in a random order without repetitions. Then, the probability that the number is divisible by 4 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

If two events $A$ and $B$ are such that $P\left( {{A^c}} \right) = 0.3,P\left( B \right) = 0.4,P\left( {A \cap {B^c}} \right) = 0.5,$ then $P\left( {B/A \cup {B^c}} \right) =$

A party is thrown for families having boys, girls, ladies and gentleman. When one member is randomly selected, odds against being a boy is $\frac{27}{5}$, odds in favour of being a girl is $\frac{7}{25}$ and probability of being a lady is $\frac{11}{32}$, then the odds in favour of the chosen person being a gentleman, 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 from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is

Let two fair six faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die A shows up four, $E_2$ is the event that $B$ shows up two and $E_3$ is the event that the sum of the numbers on both dice is odd, then which the following statements is not true?

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

$3 \%$ of the electric bulbs manufactured by a company are defective. Using Poisson distribution (approximation), the probability that a sample of 100 bulbs will contain exactly one defective, is

(Given antilog $(.1742)=1.5)$