Flashcard: Probability

Front

Define the terms experiment, sample space, and event in probability theory with examples.

Back

• Experiment: A process that leads to an outcome (e.g., rolling a die).

• Sample Space (S): The set of all possible outcomes (e.g., {1,2,3,4,5,6} for a die).

• Event (E): A subset of the sample space (e.g., rolling an even number {2,4,6}).

Front

A game involves rolling two six-sided dice. Define the sample space and find the probability of the following events:

1. 1. Getting a sum of 8.

2. 2. Rolling a double (both dice show the same number).

Back

• Sample Space (S): Since each die has 6 sides, the total number of outcomes is 6 × 6 = 36.

• Event 1: Sum of 8

• (2,6),(3,5),(4,4),(5,3),(6,2) → 5 outcomes.

  • Probability: 5/36 = 0.139
    

• Event 2: Rolling a Double

• (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) → 6 outcomes.

  • Probability: 6/36=0.167366

Front

In a class of 40 students, 25 like Mathematics, and 15 like Science. If a student is chosen randomly, what is the probability they like Mathematics?

Back

P(Mathematics)=25/40​=0.625

Front

How many ways can you arrange 5 different books on a shelf?

Back

5!=5×4×3×2×1=120.

Front

There are eight identical flags which consists of two reds, four blues and two yellows.

If all of them are to be hung up to make a signal, calculate how many distinguishable signals are there for each of the following:
a. There are no preferences.
b. The blues must be together.

Back

a. 8!/(2! 4! 2!) = 420

b. 5! / (2! 2!) = 30

Front

How many different ways can you arrange the letters of the word "SUCCESS"?

Back

7!/(3!2!)​=420

Front

If events A and B are mutually exclusive, what is P(A∪B)?

Back

P(A∪B)=P(A)+P(B)

Front

If P(A)=0.4 and P(B)=0.3, and events A and B are independent, what is P(A∩B)?

Back

P(A∩B)=0.4*0.3=0.12

Front

Given P(A)=0.6, P(B)=0.3, and P(A∣B)=0.67, find P(A∩B).

Back

P(A∩B)=0.67*0.3=0.201

Front

A class has 60 students, out of which 40 are boys. If 10 students are left-handed, and 4 of them are boys, what is the probability that a randomly selected left-handed student is a boy?

Back

P(Boy∣Left)=4/10​=0.4