What is the basic formula for probability?

P(E) = (Number of favourable outcomes) / (Total number of equally likely outcomes). This gives a value between 0 (impossible) and 1 (certain). For complementary events: P(A) + P(not A) = 1. Example: P(getting a head on a coin) = 1/2; P(getting a 3 on a die) = 1/6.

How many face cards are in a standard deck of 52 cards?

There are 12 face cards: 4 Jacks + 4 Queens + 4 Kings (one of each in every suit). Total suits = 4 (Spades, Hearts, Diamonds, Clubs), each with 13 cards (Ace to King). Red cards = 26 (Hearts + Diamonds). Aces = 4. P(face card) = 12/52 = 3/13. P(Ace) = 4/52 = 1/13.

How do you find the probability of getting a sum of 7 on two dice?

Total outcomes for 2 dice = 6 × 6 = 36. Combinations that give sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. P(sum=7) = 6/36 = 1/6. Note: sum of 7 has the highest probability among all sums (2 to 12) when throwing two dice.

Basic Probability Concepts

Probability • Class 10 Mathematics • NCERT • CBSE

Probability of an event = (Number of favourable outcomes) / (Total number of outcomes). Probability ranges from 0 (impossible) to 1 (certain). The sum of probabilities of all outcomes = 1. P(A) + P(not A) = 1.

Key Formulas

P(E) = Favourable outcomes / Total outcomes
0 ≤ P(E) ≤ 1
P(E) + P(E') = 1 (complementary events)
Total outcomes for 2 dice = 36
Total outcomes for 2 coins = 4

Frequently Asked Questions

What is the basic formula for probability?: P(E) = (Number of favourable outcomes) / (Total number of equally likely outcomes). This gives a value between 0 (impossible) and 1 (certain). For complementary events: P(A) + P(not A) = 1. Example: P(getting a head on a coin) = 1/2; P(getting a 3 on a die) = 1/6.
How many face cards are in a standard deck of 52 cards?: There are 12 face cards: 4 Jacks + 4 Queens + 4 Kings (one of each in every suit). Total suits = 4 (Spades, Hearts, Diamonds, Clubs), each with 13 cards (Ace to King). Red cards = 26 (Hearts + Diamonds). Aces = 4. P(face card) = 12/52 = 3/13. P(Ace) = 4/52 = 1/13.
How do you find the probability of getting a sum of 7 on two dice?: Total outcomes for 2 dice = 6 × 6 = 36. Combinations that give sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. P(sum=7) = 6/36 = 1/6. Note: sum of 7 has the highest probability among all sums (2 to 12) when throwing two dice.

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