Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 11 Probability Distributions Ex 11.1 Textbook Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.1

Question 1.

Suppose X is the number of tails that occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in it. inverse – images.

Solution:

Let X is the random variable that denotes the number of tails when three coins are tossed simultaneously.

Sample space S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

∴ ‘X’ takes the values 0,1, 2, 3

i.e., X (HHH) = 0 ; X (HHT, HTH, THH) = 1 ; X (HTT, THT, TTH) = 2 ; X (TTT) = 3

Question 2.

In a pack of 52 playing cards, two cards are drawn at random simultaneously. If the number of black cards drawn is a random variable, find the values of the random variable and number of points in its inverse images.

Solution:

Let X be the random variable of number of black cards occur.

∴ X = {0, 1, 2}

The sample space consists of 52C_{2} = 1326

X = 0, X (both are white cards) = 26C_{2} = 325

X = 1, X (one black and one white cards)

= 26C_{1} × 26C_{1}

= 676

X = 2, X (both are black cards) = 26C_{2} = 325

Question 3.

An urn contains 5 mangoes and 4 apples. Three fruits are taken at random. If the number of apples taken is a random variable, then find the values of the random variable and number of points in its inverse images.

Solution:

Number of mangoes = 5

Number of Apples = 4

Total number of fruits = 9

Let ‘X’ be the random variable that denotes the number of apples taken, then it takes the values 0, 1, 2, 3

X (MMM) = 0

X (AMM (or) MAM (or) MMA) = 1

X (AAM (or) AMA (or) MAA) = 2

X (AAA) = 3

Question 4.

Two balls are chosen randomly from an urn containing 6 red and 8 black balls. Suppose that we win Rs 15 for each red ball selected and we lose Rs 10 for each black ball selected. If X denotes the winning amount, then find the values of X and the number of points in its inverse images.

Solution:

Let X be the random variable that denotes the j winning amount.

X (Both are black balls) = Rs 2 (-10) = -Rs 20

X (one red and one black ball) = Rs 15 – Rs 10 = Rs 5

X (both are red ball) = Rs 2 (15) = Rs 30

∴ X = {-20, 5, 30}

The sample space consists of ^{14}C_{2} = 91

X = – 20, Both black balls = ^{8}C_{2} = 28

X = 5, One black, one red ball = ^{8}C_{1} × 6C_{1}

= 8 × 6 = 48

X = 30, Both are white balls = ^{6}C_{2} = 15

Question 5.

A six-sided die is marked ‘2’ on one face, ‘3’ on two of its faces, and ‘4’ on the remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the values of the random variable and number of points in its inverse images.

Solution:

Let X be the random variable denotes the total score is two throws of a die.

Sample Space S

n (S) = 36

X = {4, 5, 6, 7, 8}

From the sample space