Let A and B be two events such that P A ∪ B = 1 6 , P A ∩ B = 1 4 , and P A = 1 4 , where A ¯ stands for complement of event A . Then events A and B are

independent but not equally likely.

mutually exclusive and independent.

equally likely but not independent.

equally likely and mutually exclusive.

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MHT-CET

IMPORTANT

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A coin is tossed $4$ times. The probability that at least one head turns up is

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Important Questions on Probability

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Probability>Competitive Thinking>Q 35

In a throw of three dice, the probability that at least one die shows up

1

, is

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MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Probability>Competitive Thinking>Q 36

The probability that an event will fail to happen is

0.05

. The probability that the event will take place on

4

consecutive occasions is

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Probability>Competitive Thinking>Q 37

Probability of solving of sum correctly by

A, B

and

C

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

and

\frac{1}{5}

, respectively. The probability that at least one of them solves it correctly is

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Probability>Competitive Thinking>Q 38

Three players

A, B

and

C

play a game. The probability that

A, B

and

C

will finish the game are respectively

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

and

\frac{1}{4}

. The probability that the game is finished is

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MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Probability>Competitive Thinking>Q 39

There are

5

red balls and

x

black balls. If two balls are drawn at random, probability that the balls drawn are red is

\frac{5}{14}

. Find the value of

x

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MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Probability>Competitive Thinking>Q 40

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Probability>Competitive Thinking>Q 41

In four schools

B_{1}, B_{2}, B_{3}, B_{4}

the percentage of girls students is

12, 20, 13, 17

, respectively. From a school selected at random, one student is picked up at random, and it is found that the student is a girl. The probability that the school selected is

B_{2}

, is

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Probability>Competitive Thinking>Q 42

Seven White balls and three Black balls are randomly placed in a row. The probability that no two Black balls are placed adjacently equals

A coin is tossed 4 times. The probability that at least one head turns up is

Important Questions on Probability

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A coin is tossed $4$ times. The probability that at least one head turns up is