Probablity

Basic Probability Questions:

Q1.You draw a card at random from a deck that contains  3 black cards and 7 red cards.Find probablity of getting a black card?

Solution:

Total outcome = 3 black +7 red = 10

favorable outcome = 3

probability = 3/10 = 0.3

Q2. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? 

Solution:

S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) = n(E)/n(S) = 9/20.

Q3.What is the probability of getting a sum 9 from two throws of a dice?

Solution:   In 2 throws of dice, total outcome  S = 6 x 6  =36
Event of getting sum of 9( our favorable outcome)  is = (3,6),(6,3),(4,5),(5,4)
P(E) = n(E)/n(S) = 4/36 = 1/9

Q4. There are 5 marbles in a bag: 4 are blue, and 1 is red. What is the probability that a blue marble gets picked?Solution: 

P(E) = n(E)/n(S) = 4/5 = 0.8

Q5.A die is thrown once. What is the probability that the score is a factor of 6?
Solution:

The factors of six are 1, 2, 3 and 6, so the Number of ways it can happen = 4
There are six possible scores when a die is thrown, so the Total number of outcomes = 6
So the probability that the score is a factor of six = 4/6 = 2/3

Q6.A card is chosen at random from a deck of 52 playing cards. There are 4 Queens and 4 Kings in a deck of playing cards.What is the probability it is a Queen or a King?
Solution: 

There are 4 Queens and 4 Kings, so the Number of ways it can happen = 8
There are 52 cards altogether, so the Total number of outcomes = 52