Example 1. A fair die is rolled once. What is the probability of getting an even number?
- Even outcomes: 2, 4, 6, so 3 favourable out of 6.
- .
Answer:
Probability
Probability measures how likely an event is, as a number from 0 (impossible) to 1 (certain). When all outcomes are equally likely, it is the number of favourable outcomes divided by the total number of outcomes.
Formulas
Probability of an event E
Range
Complementary events
Worked examples
Example 2. A bag has 5 red, 3 blue and 2 green balls. One ball is drawn at random. Find P(blue) and P(not red).
- Total = .
- .
- .
Answer: and
Example 3. Two coins are tossed together. Find the probability of at least one head.
- The sample space is HH, HT, TH, TT: 4 outcomes.
- At least one head: HH, HT, TH, so 3 outcomes.
Answer:
Example 4. The probability that it rains tomorrow is 0.35. What is the probability that it does not rain?
- .
Answer: 0.65
Common mistakes
- Dividing favourable by unfavourable outcomes. The denominator is always the total number of outcomes.
- Giving a probability greater than 1 or less than 0, which is impossible.
- Counting outcomes that are not equally likely as if they were, for example treating "two heads, one head, no heads" as equally likely for two coins.
Practice questions with answers
1. When a fair coin is tossed once, how many possible outcomes are there?
- A1
- B2
- C3
- D4
Show answer
Answer: B) 2
A coin can land as Head or Tail, so there are 2 possible outcomes.
2. A die is thrown 300 times. The frequencies of outcomes 1, 2, 3, 4, 5 are 48, 52, 50, 47, 53. The number 6 appeared how many times?
- A100
- B50
- C45
- D55
Show answer
Answer: B) 50
Sum of others = 48 + 52 + 50 + 47 + 53 = 250. So 6 appeared 300 - 250 = 50 times.
3. The probability of any event always lies in which range?
- A0 to 1 (both inclusive)
- B0 to 100
- C-1 to 1
- D1 to 10
Show answer
Answer: A) 0 to 1 (both inclusive)
For any event E, 0 <= P(E) <= 1.
4. A coin is tossed. What is the probability of getting heads?
- A
- B
- C
- D1
Show answer
Answer: A)
A coin has two equally likely sides, so the probability of getting heads is .
5. A coin is tossed once. What is the probability of getting a head?
- A
- B1
- C0
- D
Show answer
Answer: A)
Outcomes = {H, T}, total 2. Favourable = 1 (head). .
6. In a lucky draw, tickets numbered 1 to 100 are kept in a drum at a Hyderabad mall.
One ticket is pulled out at random.
What is the probability that the ticket number is a multiple of both 4 and 5?
One ticket is pulled out at random.
What is the probability that the ticket number is a multiple of both 4 and 5?
- A
- B
- C
- D
Show answer
Answer: A)
A multiple of both 4 and 5 is a multiple of 20. From 1 to 100 these are 20, 40, 60, 80, 100 (5 tickets). Probability = .
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Practice by class
- Class 7 · Chance and Probability60 practice questions with answers
- Class 9 · Coins and Dice50 practice questions with answers
- Class 9 · Probability of an Event50 practice questions with answers
- Class 10 · Probability (Theoretical)100 practice questions with answers
- Class 10 · Probability of Simple Events50 practice questions with answers
Frequently asked questions
What is the formula for probability?
when every outcome is equally likely.
What is a sample space?
The list of all possible outcomes of an experiment, such as for a die.
What is the probability of a certain or an impossible event?
A certain event has probability 1 and an impossible event has probability 0.
What is the difference between theoretical and experimental probability?
Theoretical probability is worked out from the equally likely outcomes. Experimental probability is the fraction of times the event actually happened in trials.