MHT-CET (DEMO) CLASS 11 MATHS PROBABILITY PAPER

$$A$$ and $$B$$ are events such that $$P(A)=0.3 P(A \cup B)=0.8$$. If $$A$$ and $$B$$ are independent then $$P(B)=$$

In a $$3 \times 3$$ matrix the entries $$a_{i j}$$ are randomly selected from the digits $$\{0,1,2 \ldots 9\}$$ with replacement. The probability that the numbers of the form $$x y z$$ where $$x, y, z$$ are the elements in each row will be divisible by 11 is $$\frac{7^{K_{1}} .13^{K_{2}}}{10^{9}}$$ then $$K_{1}+K_{2}=$$ $$\qquad$$

Triangles are formed with vertices of a regular polygon of 20 sides. The probability that no side of the polygon is a side of the triangle is $$\frac{\lambda}{57}$$ Then $$\frac{\lambda}{40}$$ is $$\qquad$$

The probability that $$\sin ^{-1}(\sin x)+\cos ^{-1}(\cos y)$$ is an integer $$x, y \in\{1,2,3,4\}$$ is

Seven coupons are selected at random one at a time with replacement from 15 coupons numbered 1 to 15 . The probability that the largest number appearing on a selected coupon is 9 , is

If the letters of the word MATHEMATICS are arranged arbitrarily, the probability that C comes before E, E before $$\mathrm{H}, \mathrm{H}$$ before I and I before S is

A signal which can be green or red with probability $$\left(\frac{4}{5}\right)$$ and $$\left(\frac{1}{5}\right)$$ respectively is received by the station A and Transmitted to B. The probability each station receive signal correctly $$=\left(\frac{3}{4}\right)$$. If signal in received in $$B$$ is green. The probability original signal was green.

Three fair and unbiased dice and rolled at a time. The probability that the numbers shown are totally different.

A bag contains 7 black and 4 white balls two balls are drawn at a time from the bag. The probability at least one white ball is selected is

There are ten pairs of shoes in a cup board out or which 4 are picked up at random one after the other. The probability that there is at least one pair is

Out of 10 persons sitting at a round table. Three persons are selected at random one after the other. The chance that no two of the selected are together.

A bag contains n white and n red balls. Pairs of balls are drawn with out replacement until the bag is empty. The probability that each pair consists of one white and one red ball is

Let $$w$$ be complex cube root of unity with $$w \neq 1$$. A fair die is thrown 3 times. If $$r_{1}, r_{2}, r_{3}$$ be the numbers obtained on the die the probability that $$w^{r_{1}}+w^{r_{2}}+w^{r_{3}}=0$$ is

Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is

10 different books and 2 different pens are given to 3 boys so that each gets equal number of things. The probability that the same boy does not receive both the pens is