## 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.

Answer:

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 …………

Answer:

Not equally likely.

Question 3.

Winning in a game of carrom.

Answer:

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.

Answer:

Equally likely.

Question 5.

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

Answer:

Equally likely.

Question 6.

a) Raining on a particular day of July.

Answer:

Not equally likely.

b) Are the outcomes of every experiment equally likely?

Answer:

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.

Answer:

Equally likely events:

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

Events which are not equally likely:

- Getting a prime or composite number when a die is thrown.
- Getting an even or odd number when a card is drawn at random from a pack of cards numbered from 1 to 5.
- Getting a number which is a multiple of 3 or not a multiple of 3 from numbers 1, 2, …… 10.
- Getting a number less than 5 or greater than 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)

Answer:

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)

Answer:

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.

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.

Answer:

- When a dice is thrown, getting an even number is complementary to getting an odd number.
- Drawing a red card from a deck of cards is complementary to getting a black card.
- Getting an even number is complementary to getting an odd number from numbers 1, 2, ….. 8.
- Getting a Sunday is complementary to getting any day other than Sunday in a week.
- 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)

Answer:

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

Answer:

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)

Answer:

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)

Answer:

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)

Answer:

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)

Answer:

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)

Answer:

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?

Answer:

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.

Answer:

\(\frac{7}{2}\) 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 \(\frac{1}{3}\).

Answer:

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 \(\frac{1}{2}\).

Answer:

True.

Reason:

All possible outcomes = (1, 2, 3, 4, 5, 6) = 6

Outcomes favourable to an odd number (1, 3, 5) = 3

Outcomes favourable to an even number = (2, 4, 6) = 3

∴ Probability (odd number)

= \(\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }}\)

= \(\frac{3}{6}\) = \(\frac{1}{2}\).