Probability practice · Easy

Four fair dice $D_1, D_2, D_3$ and $D_4$ each having six faces numbered $1,2,3,4,5$ and 6 are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1, D_2$ and $D_3$, is

An urn contains 4 white and 3 red balls. There balls are drawn with replacement from this urn. Then, the standard deviation of the number of red balls drawn is

A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. The probability that the fruits are both apples or both oranges, is

Let $w$ be a complex cube root of unity with $w \neq 1$. A fair die is thrown three times. If $r_1, r_2$ and $r_3$ are the numbers obtained on the die, then the probability that $w^{r_1}+w^{r_2}+w^{r_3}=0$ is

A pack of plying cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, then the probability that the missing cards is black, is

The probability of selecting integers $a \in \left[ { - 5,30} \right]\,$ such that ${x^2} + 2\left( {a + 4} \right)x\mathrm{ } - \mathrm{ }5a\mathrm{ } + \mathrm{ }64\mathrm{ } > \mathrm{ }0,\mathrm{ }$ for all $x \in R,$ is

A coin is tossed 3 times by 2 persons. The probability that both get equal number of heads, is

A die thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared at least once is

If $A$ and $B$ are two events, such that $P\left( {A \cup B} \right) = \frac{3}{4},\;P\left( {A \cap B} \right) = \frac{1}{4},P\left( {\bar A} \right) = \frac{2}{3}$, then $P\left( {\bar A \cap B} \right)$ is equal to

Three identical dice are thrown together. The probability that distinct numbers appear on them, is

In eight throws of a die 1 or 3 is considered a success. Then, the standard deviation of success, is

Two numbers are selected randomly from the set $S=\{1,2,3,4,5,6\}$ without replacement one by one. The probability that the minimum of the two numbers is less than 4 is

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

Three groups $A, B, C$ are contesting for position on the Board of Directors of a company. The probabilities of their winning are $0.5,0.3,0.2$ respectively. If the group A wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for group $B$ and $C$ are 0.6 and 0.5 respectively. The probability that the new product will be introduced, is

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let $X$ denote the random variable of numbers of aces obtained in the two drawn cards. Then $P(X=1)+P(X=2)$ equals

It is given the events $A$ and $B$ are such that $P\left( A \right) = \frac{1}{4},P\left( {A\mathrm{|}B} \right) = \frac{1}{2}$ and $P\left( {B\mathrm{|}A} \right) = \frac{2}{3}$. Then, $P\left( B \right)$ is

Two dice are tossed 6 times. Then the probability that 7 will show an exactly four of the tosses is

A pair of a dice thrown, if 5. appears on at least one of the dice, then the probability that the sum is 10 or greater, is

If $A$ and $B$ are two independent events, then the probability that only one of $A$ and $B$ occur is

A person draws out two balls successively from a bag containing 6 red and 4 white balls. The probability that at least one of them will be red, is

Let $A$ and $B$ be two non-null events such that $A \subset B$. Then, which of the following statements is always correct.

Let $X$ be a binomially distributed random variable with mean 4 and variance $\frac{4}{3}$. Then, $54 P(X \leq 2)$ is equal to

Which of the following is true?

I. If the empty set $\phi$ and the sample space describe events, then $\phi$ is an impossible event.

II. In the above statement, the whole sample space ${S}$ is called the sure event.

An integer is chosen at random from first two hundred numbers. Then, the probability that the integer chosen is divisible by 6 or 8 is

From a pack of 52 cards, two cards are drawn one by one without replacement. The probability that first drawn card is a king and second is a queen, is

The probabilities of three events A, B and C are given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5. If $P\left( {A \cup B} \right) = 0.8,\,\,\,P\left( {A \cap C} \right) = 0.3,\,\,\,\,P\left( {A \cap B \cap C} \right) = 0.2,\,\,\,\,P\left( {B \cap C} \right) = \beta$ and $P\left( {A \cup B \cup C} \right) = \alpha ,$ where $0.85\, \le \alpha \le 0.95,$ then $\beta$ lies in the interval

The probability that a number selected at random from the set of numbers 1, 2, 3, 4, …, 100 is a cube, is

If $\mathrm{A}$ and $\mathrm{B}$ are two events such that $P(A)=\frac{4}{7}, P(A \cap B)=\frac{3}{28}$ and the conditional probability $P\left(\frac{A}{A^c \cup B^c}\right)$ (where $A^c$ denotes the compliment of the event $\mathrm{A}$ ) is equal to $\lambda$, then the value of $\frac{13}{\lambda}$ is equal to

Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is

A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. The probability that the fruits are both apples or both oranges, is