NCERT Class 10 Maths Lab Manual – Probability
Objective
To set the idea of probability of an event through a double colour cards experiment.
Prerequisite Knowledge
- Sample space and event.
- Total number of possible outcomes.
- Favourable outcomes.
- Probability of an event = \(\frac{No.offavourable\quad outcomes}{Total\quad no.of\quad Possible\quad outcomes}\).
Material Required
A cardboard of size 18 cm x 18 cm, two colour papers say pink and blue, pair of dice, empty box, pair of scissors, sketch pens, fevicol, etc.
Procedure
- Paste different colour papers, blue and pink on both sides of the board, (such that pink on one side and blue on another side)
- Divide the board into 36 small squared cards.
- Write all 36 possible outcomes obtained by throwing two dice, e.g., for the outcome (4,5), write 4 on the blue side and 5 on pink side.
- Cut and put all the cards into a box.
- Now take out each card one by one without replacement and write the observation in appropriate column.
Observation
- Total number of possible outcomes =
- Total number of favourable outcomes of sum 2 =
- Total number of favourable outcomes of sum 3 =
- Total number of favourable outcomes of sum 4 =
- Total number of favourable outcomes of sum 5=
- Total number of favourable outcomes of sum 6 =
- Total number of favourable outcomes of sum 7 =
- Total number of favourable outcomes of sum 8 =
- Total number of favourable outcomes of sum 9 =
- Total number of favourable outcomes of sum 10 =
- Total number of favourable outcomes of sum 11 =
- Total number of favourable outcomes of sum 12 =
- Total number of favourable outcomes (sum ≥11) =
- Total number of favourable outcomes (sum >12) =
- Total number of favourable outcomes (sum < 7) =
Using formula calculate the required Probability of each event.
Sample space (when two dice are thrown)
Example: Number of favourable outcomes of sum of numbers 2=1
Total outcomes = 36
∴ Probability of sum of numbers is 2 = \(\frac { 1 }{ 36 }\)
Similarly find other probabilities for different outcomes of sum.
Result
Probability of an event = \(\frac{No.offavourable\quad outcomes}{Total\quad no.of\quad Possible\quad outcomes}\)
Learning Outcome
Concept of finding the probability of an event is clear through this activity.
Activity Time
- What is the probability of getting the sum of two numbers more than 17?
- Write the sample space, when a coin is tossed 3 times.
- A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 as shown in the fig. and these are equally likely outcomes. What is the probability that it will point at
- 8?
- an odd number ?
- a number greater than 2 ?
- a number less than 9 ?
- a numberless than 1 ?
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Viva Voce
Question 1.
What is probability ?
Answer:
The possibility (or possibilites) of occuringornotoccuringof an eventis called probability.
Probability or an event = \(\frac{No.of favourable\quad outcomes}{Total\quad no.of\quad Possible\quad outcomes}\)
Question 2.
What is a sample space ?
Answer:
It is the set of all possible outcomes of a random experiment.
Question 3.
What is the probability of an impossible event, sure event respectively ?
Answer:
Zero, one.
Question 4.
A dice is thrown twice. How many elements are possible in sample space ?
Answer:
36.
Question 5.
If P(E) = 0.05, what is the probability of ‘not E’ ?
Answer:
0.95.
Question 6.
What is the sum of the probabilities of all the elementary events of an experiment ?
Answer:
One
Question 7.
A bag contains 3 red and 5 black balls. A ball is drawn at random. What is the probability that the ball is red ?
Answer:
\(\frac { 3 }{ 8 }\)
Question 8.
A die is thrown once. What is the probability of getting a prime number ?
Answer:
\(\frac { 3 }{ 6 } =\frac { 1 }{ 2 }\)
Question 9.
One card is drawn from a well shuffled deck of 52 cards. What is the probability of a king of red colour ?
Answer:
\(\frac { 2 }{ 52 } =\frac { 1 }{ 26 }\)
Multiple Choice Questions
Question 1.
A die is thrown twice. What is the probability that 5 will not come up either ?
(Hint: meaning is 5 is not coming in first throw as well as in second throw).
(a) \(\frac { 25 }{ 36 }\)
(b) \(\frac { 17 }{ 36 }\)
(c) \(\frac { 15 }{ 36 }\)
(d) None of these
Question 2.
17 cards numbered 1, 2, 3, … 17 are put in a box and mixed. One person draws a cards. Find the probability that the number on the card is prime.
(a) \(\frac { 15 }{ 17 }\)
(b) \(\frac { 7 }{ 17 }\)
(c) \(\frac { 8 }{ 17 }\)
(d) \(\frac { 9 }{ 17 }\)
Question 3.
The king, queen and jack of clubs are removed from a pack of 52 cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting ‘The ’10’ of heart’.
(a) \(\frac { 9 }{ 49 }\)
(b) \(\frac { 10 }{ 49 }\)
(c) \(\frac { 1 }{ 49 }\)
(d) None of these
Question 4.
A bag contains 5 red and some blue balls. If the probability of drawing a blue ball is double that of a red ball, find the number of blue balls in the bag.
(a) 10
(b) 5
(c) 20
(d) none of these
Question 5.
A coin is tossed three time what is the probability of getting the same result in each trial ?
(a) \(\frac { 1 }{ 4 }\)
(b) \(\frac { 1 }{ 8 }\)
(c) \(\frac { 3 }{ 8 }\)
(d) None of these
(Hint: TTT or HHH, ∴\(\frac { 2 }{ 8 } =\frac { 1 }{ 4 }\))
Question 6.
If P(E) = 0.65 then P is (\(\overset { – }{ E }\))
(a) 0.15
(b) 0.30
(c) 0.35
(d) none of these
Question 7.
Which of the following cann’t be the event of probability ?
(a) \(\frac { 2 }{ 3 }\)
(b) -1.5
(c) 15%
(d) 0.7
Question 8.
If probability of ‘not E’ is 0.98, then P(E) is
(a) 0.5
(b) 0.02
(c) 0.005
(d) 1
Question 9.
In a non-leap year there are 365 days i.e., 52 weeks and 1 day. Find the probability of getting 53 Sunday.
(a) \(\frac { 1 }{ 7 }\)
(b) \(\frac { 2 }{ 7 }\)
(c) \(\frac { 3 }{ 7 }\)
(d) None of these
Question 10.
Find the probabilitty of getting 53 Mondays in a leap year.
(a) \(\frac { 1 }{ 7 }\)
(b) \(\frac { 2 }{ 7 }\)
(c) 1
(d) none of these
Answers
- (a)
- (b)
- (c)
- (a)
- (a)
- (c)
- (b)
- (b)
- (a)
- (b)
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