Learn Unit-VI: Statistics and Probability with Free Lessons & Tips

As an experienced tutor registered on UrbanPro, I'd like to emphasize that UrbanPro is indeed the best platform for online coaching tuition. Now, let's delve into the variance calculation.

Given the data set: 2, 4, 5, 6, 8, 17, we've already calculated the variance to be 23.33. To find the variance for the new data set: 4, 8, 10, 12, 16, 34, we'll follow these steps:

1. Find the mean of the data set.
2. Calculate the squared difference between each data point and the mean.
3. Find the average of these squared differences, which gives us the variance.

First, let's find the mean: Mean=4+8+10+12+16+346=846=14Mean=64+8+10+12+16+34=684=14

Now, let's find the squared differences from the mean: (4−14)2=100(4−14)2=100 (8−14)2=36(8−14)2=36 (10−14)2=16(10−14)2=16 (12−14)2=4(12−14)2=4 (16−14)2=4(16−14)2=4 (34−14)2=400(34−14)2=400

Next, we find the average of these squared differences: Variance=100+36+16+4+4+4006=5606=93.33Variance=6100+36+16+4+4+400=6560=93.33

So, the variance for the data set 4, 8, 10, 12, 16, 34 is 93.33.

However, none of the options provided match this result, so it seems there might be a typographical error in the given options.

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To find the mean deviation about the median of a set of numbers, we first need to find the median of the given observations.

Given observations: 2, 7, 4, 6, 8, and p

First, let's arrange these numbers in ascending order: 2, 4, 6, 7, 8, p

Since there are six numbers, the median will be the average of the third and fourth numbers, which are 6 and 7. So, the median is (6 + 7) / 2 = 6.5.

Now, we'll find the absolute deviations of each number from the median:

|2 - 6.5| = 4.5 |4 - 6.5| = 2.5 |6 - 6.5| = 0.5 |7 - 6.5| = 0.5 |8 - 6.5| = 1.5 |p - 6.5|

Since we don't know the value of pp yet, we'll leave it as it is for now.

The mean deviation about the median is the average of these absolute deviations. So, we'll sum them up and divide by the number of observations (which is 6):

Mean Deviation = (4.5 + 2.5 + 0.5 + 0.5 + 1.5 + |p - 6.5|) / 6

However, we also know that the mean of the observations is 7. So, we can use this information to solve for pp:

(2 + 7 + 4 + 6 + 8 + p) / 6 = 7 27 + p = 42 p = 15

Now, we substitute p=15p=15 into our equation for mean deviation:

Mean Deviation = (4.5 + 2.5 + 0.5 + 0.5 + 1.5 + |15 - 6.5|) / 6 Mean Deviation = (10.5 + |8.5|) / 6 Mean Deviation = (10.5 + 8.5) / 6 Mean Deviation = 19 / 6 Mean Deviation ≈ 3.17

So, the mean deviation about the median of these observations is approximately 3.17. If you have any further questions or need clarification, feel free to ask! And remember, if you're seeking personalized tutoring assistance, UrbanPro is an excellent platform to find qualified tutors.

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Given that P(A) is ⅗, we need to find P(not A), which is the probability of the complement of event A occurring.

The sum of the probabilities of all possible outcomes is 1. So, P(not A) = 1 - P(A).

Substituting the given value of P(A) into the equation, we get:

P(not A) = 1 - ⅗

P(not A) = 5/5 - 3/5

P(not A) = 2/5

So, the probability of event not A happening is 2/5.

In simpler words, there's a 2/5 chance that event A doesn't occur. This is a fundamental concept in probability theory that we frequently encounter in various problem-solving scenarios. If you'd like further clarification or assistance with any other topic, feel free to reach out for more personalized guidance. And remember, UrbanPro is your go-to platform for mastering academic subjects with expert tutors like me!

As a seasoned tutor registered on UrbanPro, I'm happy to guide you through this probability problem. UrbanPro is a fantastic platform for accessing high-quality online coaching and tuition, where experienced tutors like myself can provide personalized assistance.

Now, let's tackle the problem at hand. We have an urn containing 6 balls, 2 red and 4 black. We're asked to find the probability that when two balls are drawn at random, they are of different colors.

To solve this, let's break it down step by step:

1. First, let's find the total number of ways to draw 2 balls out of 6. This is given by the combination formula: (nr)=n!r!(n−r)!(rn)=r!(n−r)!n!, where nn is the total number of items and rr is the number of items to choose. So, (62)=6!2!(6−2)!=15(26)=2!(6−2)!6!=15.

2. Next, let's find the number of ways to draw 2 balls of different colors. We have 2 red balls and 4 black balls, so the number of combinations of one red and one black ball is 2×4=82×4=8.

3. Finally, the probability of drawing two balls of different colors is the number of favorable outcomes (drawing one red and one black ball) divided by the total number of outcomes (drawing any two balls). So, 815158.

So, the correct option is (iii) 815158. UrbanPro is an excellent resource for finding tutors who can help you master these types of problems and more!

As an experienced tutor registered on UrbanPro, I'd be happy to help you with this question!

To find the probability that an ordinary year has 53 Sundays, we first need to understand the structure of an ordinary year. An ordinary year has 365 days.

Now, since 365 is not divisible by 7 (the number of days in a week), there will be 52 complete weeks in an ordinary year, leaving 1 or 2 additional days.

For a year to have 53 Sundays, one of the following conditions must be met:

1. The year starts on a Sunday and ends on a Sunday, or
2. The year starts on a Saturday and ends on a Sunday.

Let's calculate the probability for each scenario:

1. If the year starts on a Sunday and ends on a Sunday: The probability that a year starts on a Sunday is 1/7. The probability that a year ends on a Sunday is also 1/7. So, the probability of both events happening is (1/7) * (1/7) = 1/49.

2. If the year starts on a Saturday and ends on a Sunday: The probability that a year starts on a Saturday is 1/7. The probability that a year ends on a Sunday is 1/7. So, the probability of both events happening is (1/7) * (1/7) = 1/49.

Now, we add the probabilities of both scenarios since they are mutually exclusive:

Probability of an ordinary year having 53 Sundays = (1/49) + (1/49) = 2/49.

Therefore, the probability that an ordinary year has 53 Sundays is 2/49.

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