Question

Three cards are randomly selected from a deck of 52 cards. After every draw, the card is NOT replaced back in the deck. Find the probability of drawing a King, followed by two Aces in a row.

An instructor gives a pop quiz consisting of 10 multiple choice questions, where each question has 5 choices, (a) through (e). What is the probability of passing the pop quiz if you guess the answers and you have to get 8 questions correct?

The probability of event A is 0.5 and probability of event B is 0.2. Given that A and B are independent, then the probability of A and B (A intersection B) is:

How many different ways can a 9-player baseball team be selected for an informal game if there are 25 available players? Which counting method do you use?

You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a tail AND an even number on the die AND a card less than 5 (assume the ace is equal to 1) from the deck?

In a club there are 11 women and 7 men. A committee of 5 women and 3 men is to be chosen. How many different ways are there to select the committee?

If a distribution follows the binomial distribution with n = 50 and probability of success of 0.25, calculate the mean and variance.

At a raffle, 1500 tickets are being sold for $2 each. There is one prize of $500, one prize of $250, one prize of $150, and one prize of $75. If you buy one ticket, what is the expected value of your gain?

Probability is:

Choose one • 10 points

The measure of how likely an event is to occur.

The ratio of total possible outcomes to desired outcomes.

Not conveyed as a decimal or a percent.

None of the above.

Answer 1

1. Probability of a king followed by two aces = (4/52)*(4/51)*(3/50) = 0.00036

Note : There are four king , probability of drawing a king = 4/52 , after drawing first card 51 card remains and 4 ace , probability of drawing ace = 4/51 , after drawing two cards 50 cards remain and 3 ace , thus probability of drawing ace = 3/50

2. Using Binomial probability law , X be the number of correct answers

with p= 1/5 and n =10

To find , P(X 8)

Thus

  

=0.000078

Probability of passing the pop quiz =0.000078

3.If A and B are independent

P(A intersection B ) = P(A) .P(B)

=0.5*0.2

=0.1

4.Total number of players= 25

We have to select 9 players

Total number of ways to select 9 players out of 25 is =

= 2042975

5. Probability of getting a tail = 1/2 =0.5

Probability getting an even number in rolling a die = 3/6=0.5 (there are 3 odd and 3 even number in a 6 sided die)

Probability of getting a card less than 5 = 16/52= 0.3077 (there are 4 sets of number 1,2,3,4 in a pack of cards )

All these events are independent

Thus

Required probability = 0.5 *0.5 *0.3077 = 0.0769

6.Women =11

Men =7

Number of ways 5 women and 3 men are chosen =

= 16170

7. n=50 , p =0.25

mean = np = 50*0.25 = 12.5

variance = np(1-p) = 50 *0.25*0.75 = 9.375

8.Expected value of gain

= 500*(1/1500) +250*(1/1500)+150*(1/1500) +75*(1/1500) - 2

= -1.35

Expected gain = -$ 1.35

9. Probability is the measure of how likely an event is to occur

Note : probability of an event = favorable number of events / total number of events