HSC Arts (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions

For a certain data, following information is available:

Obtain the combined standard deviation

Select the correct option from the given alternatives :

If there are 10 values each equal to 10, then S.D. of these values is : ––––––––––

Select the correct option from the given alternatives :

Number of patients who visited cardiologists are 13, 17, 11, 15 in four days then standard deviation (approximately) is ______.

Answer the following :

Calculate S.D. from following data:

Answer the following :

The arithmetic mean and standard deviation of a series of 20 items were calculated by a student as 20 cms and 5 cms respectively. But while calculating them, an item 13 was misread as 30. Find the corrected mean and standard deviation

Answer the following :

The mean and S.D. of a group of 50 observations are 40 and 5 respectively. If two more observations 60 and 72 are added to the set, find the mean and S.D. of 52 items.

Answer the following :

The mean height of 200 students is 65 inches. The mean heights of boys and girls are 70 inches and 62 inches respectively and the standard deviations are 8 and 10 respectively. Find the number of boys and the combined S.D.

Answer the following :

From the following data available for 5 pairs of observations of two variables x and y, obtain the combined S.D. for all 10 observations:

Where, `sum_("i" = 1)^"n" x_"i" = 30, sum_("i" = 1)^"n" y_"i" = 40, sum_("i" = 1)^"n" x_"i"^2 = 220, sum_("i" = 1)^"n" y_"i"^2 = 340`

Answer the following :

The means and S.D. of weights and heights of 100 students of a school are as follows

Which shows more variability, weights or heights?

A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are `3/4, 1/2` and `5/8`. Find the probability that the target

1. is hit exactly by one of them
2. is not hit by any one of them
3. is hit
4. is exactly hit by two of them

The probability that a student X solves a problem in dynamics is `2/5` and the probability that student Y solves the same problem is `1/4`. What is the probability that

1. the problem is not solved
2. the problem is solved
3. the problem is solved exactly by one of them

Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery

The follwoing table summarizes their response:

If one person from the 200 patients is selected at random, determine the probability that the person was satisfied given that the person had Throat surgery.

Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery

The follwoing table summarizes their response:

If one person from the 200 patients is selected at random, determine the probability that person was unsatisfied given that the person had eye surgery

Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery.

The following table summarizes their response:

If one person from the 200 patients is selected at random, determine the probability the person had Throat surgery given that the person was unsatisfied.

Two dice are thrown together. Let A be the event 'getting 6 on the first die' and B be the event 'getting 2 on the second die'. Are the events A and B independent?

The probability that a man who is 45 years old will be alive till he becomes 70 is `5/12`. The probability that his wife who is 40 years old will be alive till she becomes 65 is `3/8`. What is the probability that, 25 years hence,

1. the couple will be alive
2. exactly one of them will be alive
3. none of them will be alive
4. at least one of them will be alive

A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, both the balls are of the same color?

A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, the balls are of different color?

Bag A contains 3 red and 2 white balls and bag B contains 2 red and 5 white balls. A bag is selected at random, a ball is drawn and put into the other bag, and then a ball is drawn from that bag. Find the probability that both the balls drawn are of same color

A bag contains 3 red and 5 white balls. Two balls are drawn at random one after the other without replacement. Find the probability that both the balls are white.

Solution: Let,

A : First ball drawn is white

B : second ball drawn in white.

P(A) = `square/square`

After drawing the first ball, without replacing it into the bag a second ball is drawn from the remaining `square` balls.

∴ P(B/A) = `square/square`

∴ P(Both balls are white) = P(A ∩ B)

`= "P"(square) * "P"(square)`

`= square * square`

= `square`