STD10 MATHS

Probability for class 10

June 17, 2022
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Topic tree

Probability – Topic Tree (Class 10 CBSE)

1. Introduction to Probability

  • Random Experiment
  • Trial and Event
  • Types of Events
    • Sure event
    • Impossible event
    • Simple event
    • Compound event

2. Theoretical Probability

Definition:

Sample Space

Equally Likely Outcomes

3. Complementary Events

4. Simple Problems on Probability

  • Coins (1 coin, 2 coins, 3 coins)
  • Dice (single die, two dice)
  • Cards (standard deck of 52 cards)
  • Marbles/balls from a bag

5. Applications of Probability

  • Everyday life problems
  • Games of chance
  • Weather, quality check, etc.

6. Key Properties

  • Probability of any event lies between 0 and 1
  • Certain and Impossible events
  • Probabilities of exhaustive events add up to 1

Probability of a desired event = number of desired events / number of elements in the total space.

Examples of probability experiments:

  • Tossing a coin
  • Playing cards
  • Throwing dice
  • Picking balls from a bag

Video Class on Probability of tossing a coin

Probability of playing cards

Basic Level Problems

  1. A fair coin is tossed twice. What is the sample space for the possible outcomes?
  2. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. A marble is randomly selected from the bag. What is the sample space for the possible outcomes?
  3. A die is rolled. What is the sample space for the possible outcomes?
  4. A deck of cards is shuffled and a card is drawn at random. What is the sample space for the possible outcomes?
  5. A roulette wheel has 38 slots, 18 of which are red, 18 are black and 2 are green. What is the sample space for the possible outcomes?
  6. A fair dice is rolled twice, What is the sample space for the possible outcomes?
  7. A bag contains 4 white balls and 6 black balls. A ball is drawn at random from the bag. What is the sample space for the possible outcomes?
  8. A spinner has four equal sections labeled A, B, C, and D. What is the sample space for the possible outcomes?
  9. A bag contains 3 red balls and 5 green balls. Two balls are drawn at random from the bag without replacement. What is the sample space for the possible outcomes?
  10. A bag contains 3 red balls, 4 blue balls and 5 green balls. Three balls are drawn at random from the bag without replacement. What is the sample space for the possible outcomes?

Keys

  1. The sample space for the possible outcomes of a fair coin tossed twice is {HH, HT, TH, TT}, where H represents heads and T represents tails.
  2. The sample space for the possible outcomes of selecting a marble from a bag containing 5 red marbles, 3 blue marbles, and 2 green marbles is {R, R, R, R, R, B, B, B, G, G}
  3. The sample space for the possible outcomes of rolling a die is {1, 2, 3, 4, 5, 6}
  4. The sample space for the possible outcomes of drawing a card from a deck of cards is {Ace of Spades, 2 of Spades, 3 of Spades, …, King of Hearts, Ace of Diamonds, 2 of Diamonds, …, King of Clubs}.
  5. The sample space for the possible outcomes of spinning a roulette wheel with 38 slots, 18 red, 18 black and 2 green is {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,00}
  6. The sample space for the possible outcomes of rolling a fair dice twice is {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
  7. The sample space for the possible outcomes of drawing a ball from a bag containing 4 white balls and 6 black balls is {W, W, W, W, B, B, B, B, B, B}
  8. The sample space for the possible outcomes of spinning a spinner with sections labeled A, B, C, and D is {A, B, C, D}.
  9. The sample space for the possible outcomes of drawing two balls from a bag containing 3 red balls and 5 green balls without replacement is {RG, RB, GB, GG, GG}
  10. The sample space for the possible outcomes of drawing three balls from a bag containing 3 red balls, 4 blue balls and 5 green balls without replacement is {RRB, RRG, RBB, RGB, RGG, BRB, BRG, BGB, BGG, GGB}.
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