Stats

1. A standard dice is rolled. What is the probability that a 2, 4, OR 6 will be rolled?

Answer : 0.5

2. Rosa will toss a fair coin twice. If you know that the first coin toss resulted in heads,what would the probability be that both coins would land on heads?

Answer : 0.5

3. 3. A spinner is divided into 3 equal sections, with sections labeled 1, 2, and 3. What is the probability of spinning a 3 on the spinner if you know the arrow landed on an odd number?

Answer : 0.5

4. A party host gives a door prize to one guest chosen at random. There are 48 men and 42 women at the party. What is the probability that the prize goes to a woman?

prob <- 42/(48+42)
print(prob)

## [1] 0.4666667

5. A spinner is divided into five equal sections numbered 1 through 5. The arrow is equally likely to land on any section

Answer : 0.2

6. Police plan to enforce speed limits during the morning rush hour on four different routes into the city. The traps on routes A, B, C, and D are operated 40% , 30%, 20%, and 30% of the time, respectively. Biff always speeds to work, and he has probability 0.2, 0.1, 0.5, and 0.2 of using those routes.
   1. What is the probability that he’ll get a ticket on any one morning?
   2. What is the probability he’ll go five mornings without a ticket?

Pa <- 0.2*0.4+0.3*0.1+0.2*0.5+0.2*0.3

7. In an urn are 5 blue, 3 red, and 2 yellow marbles. If you draw 3 marbles, what is the probability that less than 2 will be red if:

1. You draw with replacement?
2. You draw without replacement?

comb <- function(n,r){
  x = factorial(n)/((factorial(r))*(factorial(n-r)))
  return(x)
}
Pa <- (7^3)/(10^3)+(3*7*7*3)/1000
Pb <- (comb(7,3)/comb(10,3))+((comb(7,2)*3)/comb(10,3))
print(Pa)

## [1] 0.784

print(Pb)

## [1] 0.8166667

8. There are 3 urns each containing red and black marbles (see table below). You draw one marble from Urn 1. If you draw a red marble from Urn 1, you make your second draw from Urn 2. If you draw a black marble from Urn 1, you make your second draw from Urn 3. What is the probability of drawing two marbles of the same color?

P <- 7/100 + 9*5/100
print(P)

## [1] 0.52

9. A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If two marbles are drawn from the jar at random, what is the probability that one marble is white and one is red?

comb <- function(n,r){
  x = factorial(n)/((factorial(r))*(factorial(n-r)))
  return(x)
}
P = 3*10/comb(20,2)
print(P)

## [1] 0.1578947

11. You roll two 6-sided dice. What is the probability that the sum of the two dice is 10?

Answer : 0.083

12. An identification code is to consist of seven letters followed by three digits. How many different codes are possible if repetition is permitted?

code <- 26^7 + 10^3
print(code)

## [1] 8031811176

13. An 8-bit binary word is a sequence of 8 digits, of which each may be either a 0 or a 1. How many different 8-bit words are there?

bit <- 2^8
print(bit)

## [1] 256

14. Jane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Jane or Thomas is to be selected?

comb <- function(n,r){
  x = factorial(n)/((factorial(r))*(factorial(n-r)))
  return(x)
}
P = 2*comb(6,3) + comb(6,2)
print(P)

## [1] 55