HSC Science (General) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that all 3 of the sample will work.

Choose the correct option from the given alternatives:

A die is thrown 100 times. If getting an even number is considered a success, then the standard deviation of the number of successes is ______.

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The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

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For a binomial distribution, n = 5. If P(X = 4) = P(X = 3), then p = ______

For a binomial distribution, n = 4. If 2P(X = 3) = 3P(X = 2), then p = ______.

If X ~ B(4, p) and P(X = 0) = `16/81`, then P(X = 4) = ______.

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The probability of a shooter hitting a target is `3/4` How many minimum numbers of times must he fire so that the probability of hitting the target at least once is more than 0·99?

If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ______.

Let X ~ B(10, 0.2). Find P(X = 1).

Let X ~ B(10, 0.2). Find P(X ≥ 1).

Let X ~ B(10, 0.2). Find P(X ≤ 8).

The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: exactly one has a burst tyre

The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: at most three have a burst tyre

The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: two or more have burst tyre.

The probability that a lamp in a classroom will be burnt out is 0.3. Six such lamps are fitted in the class-room. If it is known that the classroom is unusable if the number of lamps burning in it is less than four, find the probability that the classroom cannot be used on a random occasion.

A lot of 100 items contain 10 defective items. Five items are selected at random from the lot and sent to the retail store. What is the probability that the store will receive at most one defective item?

A large chain retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 3%. The inspector of the retailer picks 20 items from a shipment. What is the probability that the store will receive at most one defective item?

An examination consists of 10 multiple choice questions, in each of which a candidate has to deduce which one of five suggested answers is correct. A completely unprepared student guesses each answer completely randomly. What is the probability that this student gets 8 or more questions correct? Draw the appropriate morals.

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that all 8 machines.

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that 7 or 8 machines.