# Probability

- Sample Space (S) : The set of all possible outcomes of an event
- Probability : The likeness of an event to happen
- Probability = Number of favorable outcomes / Total Number of outcomes
- 0 ≤ P ≤ 1

### Sample Problems

**Question 1 : **Three unbiased coins are tossed. What is the probability that atmost one head occurs ?

**Solution : **S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Favorable outcomes = {HTT, THT, TTH, TTT}

Total number of outcomes = 8

Number of favorable outcomes = 4

Required probability = 4 / 8 = 0.50

**Question 2 : **Find the probability of getting a red card when a card is drawn from a well shuffled pack of cards.

**Solution : **Total number of outcomes = 52

Number of favorable outcomes = Number of red cards = 26

=> Required probability = 26 / 52 = 0.50

**Question 3 : **A bag contains 6 white and 4 black balls. Two balls are drawn at random from the bag. Find the probability that both the balls are of the same color.

**Solution : **Outcome will be favorable if the two balls drawn are of the same color.

=> Number of favorable outcomes = ^{6} C _{2} + ^{4} C _{2} = 21

Total number of outcomes = ^{10} C _{2} = 45

Therefore, required probability = 21 / 45 = 7 / 15

**Question 4 : **An unbiased die is tossed. Find the probability of getting an even number.

**Solution : **S = {1, 2, 3, 4, 5, 6}

Favorable outcomes = {2, 4, 6}

Required probability = 3 / 6 = 0.50

**Question 5 : **From a bag containing red and blue balls, 10 each, 2 balls are drawn at random. Find the probability that one of them is red and the other is blue.

**Solution : **Total number of outcomes = ^{20} C _{2} = 190

Number of favorable outcomes = ^{10} C _{1} x ^{10} C _{1} = 100

Therefore, required probability = 100 / 190 = 10 / 19

### Problems on Probability | Set-2

This article has been contributed by **Nishant Arora**

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