CBSE Class 9 Mathematics Probability Set 04

Question :  In a Particular section of class IX, 40 students were asked about the months of their  birth and the following graph was prepared for the data so obtained:

Find the probability that a student of the class was born in August.

Answer:  Number of student s born in the month of August = 6

Total number of students = 40

 

 

Question : Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Answer:  Number of times 2 heads come up = 72

Total number of times the coins were tossed = 200

 

 

 

 

 

Question : An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:

 

Suppose a family is chosen, find the probability that the family chosen is

(i) earning Rs 10000 − 13000 per month and owning exactly 2 vehicles.

(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs 7000 per month and does not own any vehicle.

(iv) earning Rs 13000 − 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.

Answer:  Number of total families surveyed = 10 + 160 + 25 + 0 + 0 + 305 + 27 + 2 + 1 + 535 + 29 + 1 + 2 + 469 + 59 + 25 + 1 + 579 + 82 + 88 = 2400

 

 

 

Fill the Gap

Q1. The probability of an event can never be greater than one.
Answer: Greater
In simple words: The value of probability always lies between 0 and 1 inclusive, so it cannot exceed 1.

Exam Tip: Remember that \(0 \le P(E) \le 1\) for any event \(E\).

Q2. If the probability of happening of an event is \(\frac{3}{5}\) then the probability of not happening is \(\frac{2}{5}\).
Answer: \(\frac{2}{5}\)
Let \(E\) be the event and \(E'\) be the event of not happening.
\(P(E) + P(E') = 1\)
\(\frac{3}{5} + P(E') = 1\)
\(P(E') = 1 - \frac{3}{5} = \frac{2}{5}\)
In simple words: Subtract the given probability from 1 to find the probability of the event not occurring.

Exam Tip: Use the complementary probability formula \(P(\text{not } E) = 1 - P(E)\).

Q3. A dice is tossed once. The probability of prime number is \(\frac{1}{2}\).
Answer: \(\frac{1}{2}\)
Total possible outcomes when a die is tossed = 6 (i.e., {1, 2, 3, 4, 5, 6})
Prime numbers on a die = 3 (i.e., {2, 3, 5})
Probability = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{6} = \frac{1}{2}\)
In simple words: Count the prime numbers on a die (2, 3, 5) and divide by the total numbers (6).

Exam Tip: Note that 1 is neither prime nor composite.

Q4. In a pack of cards, the probability of red queen is \(\frac{1}{26}\).
Answer: \(\frac{1}{26}\)
Total cards in a standard deck = 52
Number of red queens = 2 (Queen of Hearts and Queen of Diamonds)
Probability = \(\frac{2}{52} = \frac{1}{26}\)
In simple words: There are 2 red queens in a deck of 52 cards, which simplifies to 1 out of 26.

Exam Tip: Total red cards are 26, divided equally into hearts and diamonds.

Q5. A box contains 25 bulbs out of which 10 are defective. The probability of non defective bulb is \(\frac{3}{5}\).
Answer: \(\frac{3}{5}\)
Total bulbs = 25
Defective bulbs = 10
Non-defective bulbs = 25 - 10 = 15
Probability of non-defective bulb = \(\frac{15}{25} = \frac{3}{5}\)
In simple words: Find the number of good bulbs (15) and divide by the total number of bulbs (25).

Exam Tip: Always subtract defective items from the total to find working or non-defective items.

Q6. A pair of dice is tossed. The probability of non doublet is \(\frac{5}{6}\).
Answer: \(\frac{5}{6}\)
Total outcomes when two dice are tossed = \(6 \times 6 = 36\)
Doublets are (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) - Total 6 doublets
Number of non-doublet outcomes = 36 - 6 = 30
Probability of non-doublet = \(\frac{30}{36} = \frac{5}{6}\)
In simple words: Subtract the 6 doublets from the 36 total outcomes to get 30 non-doublet outcomes.

Q7. If a coin is tossed 100 times then the no. of outcomes in sample space is 2.
Answer: 2
The sample space of a coin toss consists of the possible individual outcomes for a single trial, which are Head and Tail.
In simple words: A coin always has 2 possible outcomes (Head or Tail) for a single toss, regardless of how many times it is flipped.

Exam Tip: Do not confuse total outcomes in sample space (2) with total possible outcomes of 100 tosses (\(2^{100}\)).

Q8. The sum of the probabilities of all the elementary events of an experiment is 1.
Answer: 1
By definition of probability, the sum of probabilities of all possible elementary outcomes of a random experiment is always equal to 1.
In simple words: All possible outcomes combined cover 100% certainty, so their probabilities add up to 1.

Exam Tip: This is a fundamental axiom in probability theory.

Q9. The probability of an event is greater than or equal to 0 and less than or equal to 1.
Answer: 0, 1
The probability value ranges from 0 (impossible event) to 1 (sure event).
In simple words: Probabilities are always numbers between 0 and 1 inclusive.

Exam Tip: Negative probabilities or probabilities greater than 1 are mathematically impossible.

Q10. Probability of an event A + Probability of the event 'not A' is 1.
Answer: 1
\(P(A) + P(\text{not } A) = 1\)
In simple words: The chance of something happening plus the chance of it not happening always equals 1.

Exam Tip: This rule is very useful for finding complementary probabilities quickly.

Q11. A coin is tossed once, its sample space is/are {H, T}.
Answer: {H, T}
When a single coin is tossed, the possible outcomes are Head (H) and Tail (T).
In simple words: The set of all possible results is Head and Tail, written as {H, T}.

Exam Tip: Always enclose sample spaces in curly braces.

Q12. A dice is tossed once. The probability of 7 is 0.
Answer: 0
A standard die has faces numbered 1 through 6. Getting a 7 is impossible.
In simple words: Since 7 is not on a die, the probability of rolling a 7 is zero (impossible event).

Exam Tip: The probability of any impossible event is always 0.