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A company has two plants $P_1$ and $P_2$ which produces 60% and 40% of pens respectively. At plant $P_1$ 80% of pens are rated of grade A and at plant $P_2$ 90% of pens are rated of grade A. A pen is picked up at random and is found to be of grade A. The probability that it has manufactured from plant $P_1$ is:

Bag I contains 4 red and 3 black balls and bag II contains 6 red and 5 black balls. One ball is drawn at random from one of the bags, the probability that it is a red ball, is

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X denotes the number of Spades in two draws, then

Match the LIST-I with LIST-II

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If $P(A \cap B) = \frac{1}{2}$, $P(A' \cap B') = \frac{1}{3}$, $P(A) = p$ and $P(B) = 2p$, then value of $p$ is

A man is known to speak the truth 3 out of 4 times. He throw a die and reports that it is five then the probability that it is actually five is

Let A and B be independent events such that $P(A) = \frac{3}{7}$ and $P(B) = \frac{1}{7}$, Then

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A problem is given to 3 students A,B and C, whose probabilities of solving are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively, then

(A). P(Problem solved) = $\frac{3}{4}$

(B). P(Problem not solved) = $\frac{1}{4}$

(C). P(Problem solved by exactly one student) = $\frac{7}{24}$

(D). P(Problem solved by at least 2 students) = $\frac{17}{24}$

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A pair of dice is thrown. If the two numbers appearing on them are different then the probability that the sum of the number is 6, is.

A fair coin is tossed until a head or five tails occur. The probability distribution of the number of tosses is,

Two dice are thrown then the probability of the sum of numbers appearing to be prime is :

A random variable X has the following probability distribution:

The value of K is

During a season change, a pathologist observed that out of 10,000 people tested for viral fever, 1000 people were tested positive. Then the standard deviation for the distribution of positive reports is_______

A die is thrown thrice. If the first throw is a four, then the chance of getting 11 as total sum, is

A coin is tossed thrice, and events E and F are defined as:

E : "The first throw results in a head"

F : "The last throw results in tail"

Then, which of the following statements is true for events E and F?

A coin is tossed four times. The probability of getting atleast 1 head before getting the first tail is

A beg contains 4 white and 6 red balls. Four balls are drawn at random, then match the probability of the numbers of white balls drawn. Where P(E) denotes the probability of an event E.

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4 cards are drawn from a standard deck of 52 cards. The probability of drawing exactly 2 cards of the same suit is:

A coin is tossed 5 times, the probability of getting at least 3 heads is:

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

A man is known to speak truth 8 out of 11 times. He takes out two balls from a bag containing 3 white, 2 black and 5 red balls. What is the probability that he reports both the balls to be white?

Match List-I with List-II

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A man speaks the truth 8 out of 10 times. A die is tossed. He reports that it was 5. What is the probability that it was actually 5?

Two thirds of the students in a class are boys and the rest are girls. It is known that the probability of a girl getting a first class is 0.25 and that of a boy getting a first class is 0.28, then the probability that a student chosen at random will get first class marks in the subject is

The random variable X has the following probability distribution:

The correct value of k is:

The monthly expectation of a two-wheeler accident at a particular railway crossing is 0.02. What is the probability that in a specific month, no accident occurred? (given $e^{-0.02} = 0.9802$)

Two cards are drawn successively with replacement from a well shuffled pack of 52 playing cards. Which of the following is correct probability distribution of number of Queens(X) as $\binom{X}{P(X)}$?

If $P(A) = 0.4$, $P(B) = X$ and $P(\bar{A} \cap \bar{B}) = 0.4$, where A and B are independent event, then the value of X is:

If A and B are independent events such that $P(A)=\dfrac{1}{2}$, $P(A\cup B)=\dfrac{3}{5}$ and $P(B)=p$, then value of p is:

One ticket is drawn from a purse containing four tickets with numbers 223, 133, 212, 322. Let $A_i$ be the event that i$^{th}$ digit of the number on drawn ticket is 2. Then which of the following events are independent ?

A. $A_1$ and $A_2$

B. $A_2$ and $A_3$

C. $A_1$ and $A_3$

D. $A_1$, $A_2$ and $A_3$

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A farmer has a tubewell which works by connecting two switches $S_1$ and $S_2$. The probability that $S_1$ works is 9/10 and the probability that $S_2$ works is 8/10. The farmer connects them in series in 30% cases and in parallel in 70% cases. If it is known that the tubewell was working, what is the probability that it was a series connection.