Two dice are thrown independently. Let A be the event that the number appeared on the 1 st die is less than the number appeared on the 2 nd die, B be the event that the number appeared on the 1 st die is even and that on the second die is odd, and C be the event that the number appeared on the 1 st die is odd and that on the 2 nd is even. Then

The number of favourable cases of the event ( A ∪ B ) ∩ C is 6

The number of favourable cases of the events A , B and C are 15 , 6 and 6 respectively

MEDIUM

JEE Main

IMPORTANT

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The probabilities of three events $A, B$ and $C$ are given $P (A) = 0.6, P (B) = 0.4$ and $P (C) = 0.5$ . If $P (A \cup B) = 0.8, P (A \cap C) = 0.3, P (A \cap B \cap C) = 0.2, P (B \cap C) = β$ and $P (A \cup B \cup C) = α$ , where $0.85 \leq α \leq 0.95,$ then $β$ lies in the interval :

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Important Questions on Probability

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 7th January 2020 Shift 1>Q 43

An unbiased coin is tossed

5

times. Suppose that a variable

X

is assigned the value

k

when

k

consecutive heads are obtained for

k = 3, 4, 5,

otherwise

X

takes the value

- 1 .

Then the expected value of

X,

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 7th January 2020 Shift 2>Q 44

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is

\frac{1}{4}

. If the probability that at most two machines will be out of service on the same day is

{(\frac{3}{4})}^{3} k,

then

k

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 8th January 2020 Shift 1>Q 45

Let

A

and

B

be two independent events such that

P (A) = \frac{1}{3}

and

P (B) = \frac{1}{6} .

Then, which of the following is true?

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 8th January 2020 Shift 2>Q 46

Let

A

and

B

be two events such that the probability that exactly one of them occurs is

\frac{2}{5}

and the probability that

A

B

occurs is

\frac{1}{2}

, then the probability of both of them occur together is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 9th January 2020 Shift 1>Q 47

In a box, there are

20

cards, out of which

10

are labelled as

A

and the remaining

10

are labelled as

B

. Cards are drawn at random, one after the other and with replacement, till a second

A

card is obtained. The probability that the second

A

card appears before the third

B

card is:

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 9th January 2020 Shift 2>Q 48

10

different balls are to be placed in

4

distinct boxes at random, then the probability that two of these boxes contain exactly

2

and

3

balls is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 9th January 2020 Shift 2>Q 49

A random variable

X

has the following probability distribution:

\begin{matrix} \begin{matrix} X : & 1 & \begin{matrix} 2 & 3 & \begin{matrix} 4 & 5 \end{matrix} \end{matrix} \end{matrix} \\ P (X) : \begin{matrix} k^{2} & \begin{matrix} 2 k & k & \begin{matrix} 2 k & 5 k^{2} \end{matrix} \end{matrix} \end{matrix} \end{matrix}

Then,

P (X > 2)

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Probability>JEE Main - 9th April 2019 Shift 1>Q 50

Four persons can hit a target correctly with probabilities

\frac{1}{2}, \frac{1}{3}, \frac{1}{4}

and

\frac{1}{8}

respectively. If all hit at the target independently, then the probability that the target would be hit, is

The probabilities of three events A,B and C are given PA=0.6, PB=0.4 and PC=0.5. If PA∪B=0.8, PA∩C=0.3, PA∩B∩C=0.2, PB∩C=β and PA∪B∪C=α, where 0.85≤α≤0.95, then β lies in the interval :

Important Questions on Probability

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The probabilities of three events $A, B$ and $C$ are given $P (A) = 0.6, P (B) = 0.4$ and $P (C) = 0.5$ . If $P (A \cup B) = 0.8, P (A \cap C) = 0.3, P (A \cap B \cap C) = 0.2, P (B \cap C) = β$ and $P (A \cup B \cup C) = α$ , where $0.85 \leq α \leq 0.95,$ then $β$ lies in the interval :