Question

Compute the following probabilities. Express your answer as a decimal, rounded to three decimal places.

1. (a) Chris has 6 t-shirts, 3 pairs of pants, and 1 pair of underwear. Assuming he chooses what to wear randomly and washes his clothes every day (hopefully), what is the probability of him wearing the exact same outfit two days in a row?

2. (b) Three distinct six sided dice are rolled, what is the probability that the sum of the three dice is five?

3. (c) Given a standard deck of cards, what is the probability of randomly selecting a queen or a heart, twice in a row (with replacement)?

4. (d) You roll a six-sided die 12 times. What is the probability of landing on a 6 more than 5 times?

5. (e) It is estimated that one in ten Americans are left-handed. Given 30 randomly selected Americans, what is the probability that 3 of them will be left-handed?

Answer 1

a)The probability of him wearing the exact same outfit two days in a row=

b)Total number of outcomes=6³=216

Outcomes in which the sum of three dice is five=S={(1,1,3),(1,3,1),(3,1,1),(1,2,2),(2,1,2),(2,2,1)}

n(S)=6

The probability that the sum of the three dice is five=

c)The probability of randomly selecting a queen or a heart, twice in a row(with replacement)=

d)The probability of landing on a 6 more than 5 times when a 6 sided die is rolled 12 times =

e)p=0.1

n=30

x=3

The probability that 3 of them will be left-handed=