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Maths 3 Mark Question

Data Handling - IV (Probability) · Maharashtra Board STD 8 (MSBSHSE - English Medium). 5 questions.

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3 Mark Question

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5 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
A bag contains 5 red marbles, 8 white marbles, 4 green marbles. What is the probability that if one marble is taken out of the bag at random, it will be
  1. red
  2. white
  3. not green
Answer
Number of red marbles = 5
Number of white marbles = 8
Number of green marbles = 4
Total number of marbles in the bag = 5 + 8 + 4 = 17
$\therefore$ Total number outcomes = 17
  1. Let A be the event of drawing a red ball.
$\therefore\text{ P(A)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{5}{17}$
  1. Let B be the event of drawing a white ball.
$\therefore\text{ P(B)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{8}{17}$
  1. Let C be the event of drawing a green ball.
$\therefore\text{ P(C)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{4}{17}$

Now, the event of not drawing a green ball is:

$\text{P}(\bar{\text{C}}) = 1 −\text{ P(C)} = 1 − \frac{4}{17} = \frac{13}{17}$
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Question 23 Marks
If you have a collection of 6 pairs of white socks and 3 pairs of black socks. What is the probability that a pair you pick without looking is
  1. white?
  2. black?
Answer
Number of pairs of white socks = 6
Number of pairs of black socks = 3
Total number of pairs of socks = 6 + 3 = 9
$\therefore$ Number of possible outcomes = 9
Let A be the event of getting a pair of white socks.
$ \therefore\text{P(A)}=\frac{6}{9}=\frac{2}{3}$
Let B be the event of getting a pair of black socks.
$ \therefore\text{P( B)}=\frac{3}{9}=\frac{1}{3}$
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Question 33 Marks
If you have a spinning wheel with 3-green sectors, 1-blue sector and 1-red sector. What is the probability of getting a green sector? Is it the maximum?
Answer
Number of green sectors in the wheel = 3
Number of blue sectors in the wheel = 1
Number of red sectors in the wheel = 1
Total number of sectors in the wheel = 3 + 1 + 1 = 5
$\therefore$ Number of possible outcomes = 5
$\therefore\text{P(A)}=\frac{3}{5}, \text{P(B)}=\frac{1}{5} \text{and}\text{ P(C)}=\frac{1}{5}$
Hence, the probability of getting a green sector is the maximum.
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Question 43 Marks
If you put 21 consonants and 5 vowels in a bag. What would carry greater probability? Getting a consonant or a vowel? Find each probability.
Answer
Number of consonants = 21
Number of vowels = 5
Total number of possible outcomes = 21 + 5 = 26
Let C be the event of getting a consonant and V be the event of getting a vowel.
$\therefore\text{P(C)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{21}{26}$
$\text{And,} \ \text{P(C)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{5}{26}$
Thus, the consonants have a greater probability.
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Question 53 Marks
A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is:
  1. red
  2. black
Answer
Number of red balls = 3
Number of black balls = 5
Total number of balls = 3 + 5 = 8
Let A be the event of drawing a red ball.
$\therefore\text{ P(A)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{3}{8}$
Let B be the event of drawing a black ball.
$\therefore\text{ P( B)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{5}{8}$
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