Mathematics Crash Course MHT-CET>Chapter 29 - Binomial Distribution>Exercise 1>Q 8

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IMPORTANT

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A fair coin is tossed at a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

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Important Questions on Binomial Distribution

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Mathematics Crash Course MHT-CET>Chapter 29 - Binomial Distribution>Exercise 1>Q 9

A die is thrown thrice, then the probability of getting an odd number atleast once is

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Mathematics Crash Course MHT-CET>Chapter 29 - Binomial Distribution>Exercise 1>Q 10

The number of ways in which

16

identical things can be distributed among

4

persons if each person get atleast

3

things is

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Mathematics Crash Course MHT-CET>Chapter 29 - Binomial Distribution>Exercise 1>Q 11

Consider

5

independent Bernoulli’s trials each with probability of success

p

. If the probability of at least one failure is greater than or equal to

\frac{31}{32},

then

p

lies in the interval

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Mathematics Crash Course MHT-CET>Chapter 29 - Binomial Distribution>Exercise 1>Q 12

Let

C_{1}

and

C_{2}

be two biased coins such that the probabilities of getting head in a single toss are

\frac{2}{3}

and

\frac{1}{3}

, respectively. Suppose

α

is the number of heads that appear when

C_{1}

is tossed twice, independently, and suppose

β

is the number of heads that appear when

C_{2}

is tossed twice, independently. Then the probability that the roots of the quadratic polynomial

x^{2} - α x + β

are real and equal, is

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Mathematics Crash Course MHT-CET>Chapter 29 - Binomial Distribution>Exercise 1>Q 13

An experiment succeeds twice as often as it fails. The probability that in the next six trials there are at least

4

successes is

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Mathematics Crash Course MHT-CET>Chapter 29 - Binomial Distribution>Exercise 1>Q 14

The mean and standard deviation of a binomial variate

X

are

4

and

\sqrt{3}

respectively. Then,

P (X \geq 1)

is

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Mathematics Crash Course MHT-CET>Chapter 29 - Binomial Distribution>Exercise 1>Q 15

If three different dice are rolled three times, then the probability that they show three different numbers exactly twice is equal to

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Mathematics Crash Course MHT-CET>Chapter 29 - Binomial Distribution>Exercise 1>Q 16

The probability that an event does not happen in a trial is

0.8.

The probability that the event happens at most once in three trails is