math 111 probabilities

[subtle]

A bin contains 20 batteries, of which 3 are defective, (so 17 are good). If you select 2 at random find the probability that:

a. both are good - with replacement and without replacement.

B. the 1st is defective and the 2nd is defective.
C. The 1st is good but the 2nd is defective.
D. At least one is defective.
E. Exactly one is good.

Hi, please help with these questions.

The circle is divided into 4 equal areas with $10 in one section in $1 in the other three. If the spinner is spun twice, find the probability the pointer lands on:

a. $1 twice.
b. $10 first and then $ second.
c. $10 once and $1 once.
d. $10 at least once.

If the player pays $5 to spin twice and wins the larger of the two values the pointer lands on, find her expectation.

 

[tkhunny]

A bin contains 20 batteries, of which 3 are defective, (so 17 are good). If you select 2 at random find the probability that:

These are just counting problems. You can invent fancy formulas for them, but I suspect it will be OK to save that for the next unit.

a. both are good - with replacement and without replacement.

Pr(1st is good) = 17/20
Pr(2nd is Good(without replacement)) = 16/19 (One fewer in the bin and one fewer good one.)
Pr(2nd is Good(WITH replacement)) = 17/20 (We put it back. Why would it be different?)
Pr(Both are good withOUT replacement) = (17/20)*(16/19)
Pr(Both are good WITH replacement) = (17/20)*(17/20)

B. the 1st is defective and the 2nd is defective.
C. The 1st is good but the 2nd is defective.
D. At least one is defective.
E. Exactly one is good.

The only one that is a little tricky is D. "at least one" means 1 or 2, in this case.

The circle is divided into 4 equal areas with $10 in one section in $1 in the other three. If the spinner is spun twice, find the probability the pointer lands on:

a. $1 twice.
b. $10 first and then $ second.
c. $10 once and $1 once.
d. $10 at least once.

These are just "with replacement" problems. Give them some thought and show us what your get.