Question

Let the random variable X be the outcome of rolling a 6-sided die. Assuming the die is fair, the probability distribution is as follows:
X 1 2 3 4 5 6
Probability 1/6 1/6 1/6 1/6 1/6 1/6
Using the above table,the probability that X is less than or equal to 2 is:
A.1/6
B.1/5
C.1/3
D.1/2
E.2/3

Answer 1

is it C? i just need confirmation @perl

Answer 2

can you show me your reasoning

Answer 3

1 and 2 are the only ones less than or equal to 2 so it would be 2/6 and simplifies to 1/3

Answer 4

P( X<=2 ) = P( X =1 or X=2) = P(X=1) + P(X=2) = 1/6 + 1/6

Answer 5

so you did it right .

Answer 6

okay great thank you! i need help with another is that okay?

Answer 7

ok

Answer 8

Which of the following represents the sample space for rolling a 6-sided die and tossing a coin?

A. {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}
B. {1, 2, 3, 4, 5, 6}
C. {H, T}
D. {1, 2, 3, 4, 5, 6, H, T}

Answer 9

what is your intuition say

Answer 10

i think its B because a sample space is the set of all possible outcomes

Answer 11

*D

Answer 12

does b) mention a coin, heads or tails?

Answer 13

i meant D

Answer 14

almost.
we want to show you roll a die *and* a coin.
so for example 1H would be a sample point.

Answer 15

so it would A?

Answer 16

you can think of them as simultaneous events, you roll a die at the same time as flipping a coin

Answer 17

right

Answer 18

okay thank you! can you check my work on this?
If P (A) = 0.2 and P (B) = 0.3 and A and B are independent but NOT disjoint, find P (A or B).

A 0.06
B 0.10
C 0.44
D 0.50
E Cannot be determined from the information given.

i say A because its independent you do (.2)(.3) = 0.06

Answer 19

what do you think? i say A because its independent you do (.2)(.3) = 0.06

Answer 20

@perl

Answer 21

one moment

Answer 22

ok

Answer 23

The general 'or' formula is :

P(A or B ) = P(A) + P(B) - P( A & B )

Answer 24

i get 0.44

Answer 25

okay thank you! can you check my work on this?
If P (A) = 0.2 and P (B) = 0.3 and A and B are independent but NOT disjoint, find P (A or B).

P(A or B) = P(A) + P(B) - P(A & B )
because A,B are independent
P(A or B) = P(A) + P(B) - P(A) *P(B)
= 0.2 + 0.3 - (0.2)*(0.3)

Answer 26

yes thats correct

Answer 27

okay sorry can you check one more?

Answer 28

Let the random variable X be the outcome of rolling a 6-sided die. Assuming the die is fair, the probability distribution is as follows:
X 1 2 3 4 5 6
Probability 1/6 1/6 1/6 1/6 1/6 1/6

Using the table of probabilities above,what is the probability of rolling a value greater than 3?
A. 1/6
B. 1/4
C. 1/3
D. 1/2
E. 1

Answer 29

I said 1/6 because the probability of getting any number 1/6
or would it be 1/3 because we leave the numbers 3 and under out

Answer 30

P(X > 3)
= P( X = 4 or X = 5 or X = 6)
= P( X = 4) + P(X = 5) + P( X = 6)
= 1/6 + 1/6 + 1/6

Answer 31

so 1/3 is correct?

Answer 32

@perl

Answer 33

yes

Answer 34

okay thank you so much!! you're amazing as always

Answer 35

Your welcome .