## AP State Syllabus SSC 10th Class Maths Solutions 13th Lesson Probability InText Questions

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 13 Probability InText Questions and Answers.

### 10th Class Maths 13th Lesson Probability InText Questions and Answers

Do This

(Page No. 307)

Outcomes of which of the following experiments are equally likely ?
Question 1.
Getting a digit 1, 2, 3, 4, 5 or 6 when a die is rolled.
Equally likely. Question 2.
Picking a different colour ball from a bag of 5 red balls, 4 blue balls and 1 black ball.
Note: Picking two different colour balls …………..
i.e., picking a red or blue or black ball from a …………
Not equally likely.

Question 3.
Winning in a game of carrom.
Equally likely.

Question 4.
Units place of a two digit number selected may be 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.
Equally likely.

Question 5.
Picking a different colour ball from a bag of 10 red balls, 10 blue balls and 10 black balls.
Equally likely.

Question 6.
a) Raining on a particular day of July.
Not equally likely.

b) Are the outcomes of every experiment equally likely?
Outcomes of all experiments need not necessarily be equally likely.

c) Give examples of 5 experiments that have equally likely outcomes and five more examples that do not have equally likely outcomes.
Equally likely events:

1. Getting an even or odd number when a die is rolled.
2. Getting tail or head when a coin is tossed.
3. Getting an even or odd number when a card is drawn at random from a pack of cards numbered from 1 to 10.
4. Drawing a green or black ball from a bag containing 8 green balls and 8 black balls.
5. Selecting a boy or girl from a class of 20 boys and 20 girls.
6. Drawing a red or black card from a deck of cards.

Events which are not equally likely:

1. Getting a prime or composite number when a die is thrown.
2. Getting an even or odd number when a card is drawn at random from a pack of cards numbered from 1 to 5.
3. Getting a number which is a multiple of 3 or not a multiple of 3 from numbers 1, 2, …… 10.
4. Getting a number less than 5 or greater than 5.
5. Drawing a white ball or green ball from a bag containing 5 green balls and 8 white balls. Question 7.
Think of 5 situations with equally likely events and find the sample space.    (Page No. 309)
a) Tossing a coin: Getting a tail or head when a coin is tossed.
Sample space = {T, H}.
b) Getting an even or odd number when a die is rolled.
Sample space = (1, 2, 3, 4, 5, 6}.
c) Winning a game of shuttle.
Sample space = (win, loss}.
d) Picking a black or blue ball from a bag containing 3 blue balls and 3 blackballs = {blue, black}.
e) Drawing a blue coloured card or black coloured card from a deck of cards = {black, red}.

Question 8.
i) Is getting a head complementary to getting a tail? Give reasons.   (Page No. 311)
Number of outcomes favourable to head = 1
Probability of getting a head = $$\frac{1}{2}$$ [P(E)]
Number of outcomes not favourable to head = 1
Probability of not getting a head = $$\frac{1}{2}$$ [P($$\overline{\mathrm{E}}$$)]
Now P(E) + P($$\overline{\mathrm{E}}$$) = $$\frac{1}{2}$$ + $$\frac{1}{2}$$ = 1
∴ Getting a head is complementary to getting a tail.

ii) In case of a die is getting a 1 comple-mentary to events getting 2, 3, 4, 5, 6? Give reasons for your answer.
Yes. Complementary events.
∵ Probability of getting 1 = $$\frac{1}{6}$$ [P(E)]
Probability of getting 2, 3, 4, 5, 6 = P(E) = P($$\overline{\mathrm{E}}$$) = $$\frac{5}{6}$$
P(E) + P($$\overline{\mathrm{E}}$$) = $$\frac{1}{6}$$ + $$\frac{5}{6}$$ = $$\frac{6}{6}$$ = 1

iii) Write of five new pair of events that are complementary.

1. When a dice is thrown, getting an even number is complementary to getting an odd number.
2. Drawing a red card from a deck of cards is complementary to getting a black card.
3. Getting an even number is complementary to getting an odd number from numbers 1, 2, ….. 8.
4. Getting a Sunday is complementary to getting any day other than Sunday in a week.
5. Winning a running race is complementary to loosing it. Try This

Question 1.
A child has a dice whose six faces show the letters A, B, C, D, E and F. The dice is thrown once. What is the probability of getting (i) A? (ii) D?     (Page No. 312)
Total number of outcomes (A, B, C, D, E and F) = 6.
i) Number of favourable outcomes to A = 1
Probability of getting A =
P(A) = $$\frac{\text { No.of favourable outcomesto } \mathrm{A}}{\text { No.of all possible outcomes }}$$ = $$\frac{1}{6}$$

ii) No. of outcomes favourable to D = 1
Probability of getting D
= $$\frac{\text { No.of outcomes favourble to } \mathrm{D}}{\text { All possible outcomes }}$$ = $$\frac{1}{6}$$

Question 2.
Which of the following cannot be the probability of an event?     (Page No. 312)
(a) 2.3
(b) -1.5
(c) 15%
(d) 0.7
a) 2.3 – Not possible
b) -1.5 – Not possible
c) 15% – May be the probability
d) 0.7 – May be the probability

Question 3.
You have a single deck of well shuffled cards. Then, what is the probability that the card drawn will be a queen?     (Page No. 313)
Number of all possible outcomes = 4 × 13 = 1 × 52 = 52
Number of outcomes favourable to Queen = 4 [♥ Q, ♦ Q, ♠ Q, ♣ Q]
∴ Probability P(E) = $$\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }}$$
= $$\frac{4}{52}$$ = $$\frac{1}{13}$$ Question 4.
What is the probability that it is a face card?     (Page No. 314)
Face cards are J, Q, K.
∴ Number of outcomes favourable to face card = 4 × 3 = 12
No. of all possible outcomes = 52
P(E) = $$\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }}$$
= $$\frac{12}{52}$$ = $$\frac{3}{13}$$

Question 5.
What is the probability that it is a spade?       (Page No. 314)
Number of spade cards = 13
Total number of cards = 52
Probability
= $$\frac{\text { Number of outcomes favourable to spades }}{\text { Number of all outcomes }}$$
= $$\frac{13}{52}$$ = $$\frac{1}{4}$$

Question 6.
What is the probability that is the face card of spades?       (Page No. 314)
Number of outcomes favourable to face cards of spades = (K, Q, J) = 3
Number of all outcomes = 52
P(E) = $$\frac{3}{52}$$

Question 7.
What is the probability it is not a face card?       (Page No. 314)
Probability of a face card = $$\frac{12}{52}$$ from (1)
∴ Probability that the card is not a face card (or)
Number of favourable outcomes = 4 × 10 = 40
Number of all outcomes = 52
∴ Probability
= $$\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }}$$
= $$\frac{40}{52}$$ = $$\frac{10}{13}$$ Think & Discuss

(Page No. 312)

Question 1.
Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of any game?
Probability of getting a head is $$\frac{1}{2}$$ and of a tail is $$\frac{1}{2}$$ are equal.
Hence tossing a coin is a fair way.

Question 2.
Can $$\frac{7}{2}$$ be the probability of an event? Explain.
$$\frac{7}{2}$$ can’t be the probability of any event.
Since probability of any event should lie between 0 and 1.

Question 3.
Which of the following arguments are correct and which are not correct? Give reasons.
i) If two coins are tossed simultaneously, there are three possible outcomes – two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $$\frac{1}{3}$$.
False.
Reason:
All possible outcomes are 4
HH, HT, TH, TT
Thus, probability of two heads = $$\frac{1}{4}$$
Probability of two tails = $$\frac{1}{4}$$
Probability of one each = $$\frac{2}{4}$$ = $$\frac{1}{2}$$. ii) If a dice is thrown, there are two possible outcomes – an odd number or an even number. Therefore, the probability of getting an odd number is $$\frac{1}{2}$$.
= $$\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }}$$
= $$\frac{3}{6}$$ = $$\frac{1}{2}$$.