Question

1. Let’s assume you have a bag of balls (5 red and 5 black). You roll a six-sided dice and then select a ball from the bag.
   1. What is the probability you roll a five on the die and then select a red ball?
2. You are playing blackjack with no other players (i.e. cards are dealt immediately with no one else receiving cards). What is the probability you get a K, Q, J, or 10 on the first card followed by an ace on the second card? (No replacement)
3. The Powerball Lottery requires you to select 5 numbers between 1 and 69 and 1 number between 1 and 26. What is the probability of selecting ALL numbers correct? (Please show your work).

Answer 1

a) . Probability of getting a 5 on the dice = 1/6

Probability of getting a red ball = 5C1 / 10C1

= 5/10

= 1/2

Probability of happening both = 1/6*1/2

= 1/12

b) .  probability of getting

J Q K or 10 = no. Favourable cards / total cards

Number of cards as J K Q and 10 = 16

Number of total cards = 52

Probability = 16/52

Number ace cards = 4

Number of remaining cards = 51

Probability of getting an ace = 4/51

Probability of getting J Q K or 10 in 1st card and ace in 2nd card is given as ,

P = 16/52*4/51

= 64 / 2652

c) .   Number of combination of 5 numbers drawn from 1- 69 is given by

=

= 1348621560/ 120

= 11238513

In which only 1 combination is correct and the probability of getting the correct combination is given as

= 1 / 11238513

The number of combination of 1 number drawn from the set from 1 - 26 is

=

=

= 26

In which only one is correct and probability of getting the correct number is

= 1 / 26

The probability of getting all number correctly is obtained by multiplying the two

= (1/11238513) * (1/26)

= 1/ 292201338

=