Coin toss problem

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Jan 22nd 2008, 11:51 AM
sarahh

Coin toss problem

1). In 3 fair coin tosses, what is the probability of obtaining exactly 2 tails? (Note In a fair coin toss the 2 outcomes, heads and tails, are equally likely).

I don't understand why the answer is 3/8??

2). In a shipment of 1000 light bulbs, 1/40 of the bulbs were defective. What is the ratio of defective bulbs to non-defective bulbs?

Why is the answer 1/39??
Jan 22nd 2008, 12:02 PM
colby2152

Quote:

Originally Posted by sarahh

1). In 3 fair coin tosses, what is the probability of obtaining exactly 2 tails? (Note In a fair coin toss the 2 outcomes, heads and tails, are equally likely).

I don't understand why the answer is 3/8??

Exactly two tails means two tails AND one head. There are three different ways that possibility can occur. $3*\left(\frac{1}{2}\right)^3 = \frac{3}{8}$

Quote:

Originally Posted by sarahh

2). In a shipment of 1000 light bulbs, 1/40 of the bulbs were defective. What is the ratio of defective bulbs to non-defective bulbs?

Why is the answer 1/39??

The amount of light bulbs is useless information... $\frac{\frac{1}{40}}{\frac{39}{40}}=\frac{1}{39}$
Jan 22nd 2008, 12:15 PM
sarahh

Thanks so much colby--lol number 2 can't believe I didn't see that. Still a little stuck on the first...not sure why it's 3 times a half cubed??
Jan 22nd 2008, 12:19 PM
colby2152

Quote:

Originally Posted by sarahh

Thanks so much colby--lol number 2 can't believe I didn't see that. Still a little stuck on the first...not sure why it's 3 times a half cubed??

Three possibilities; there are three coin tosses that can go like this:

TTH
HTT
THT

Each one of those has a $\frac{1}{8}$ chance of happening.
Jan 22nd 2008, 12:25 PM
sarahh

Ahh ok--so the reason why it's over 8 is because of the other 5 possibilities?? That is:

HHH
TTT
THH
HTH
HHT
Jan 22nd 2008, 12:28 PM
colby2152

Quote:

Originally Posted by sarahh

Ahh ok--so the reason why it's over 8 is because of the other 5 possibilities?? That is:

HHH
TTT
THH
HTH
HHT

Yes, as always in probability, that is one more way of looking at it! (Handshake)
Jan 23rd 2008, 04:22 AM
mr fantastic

Quote:

Originally Posted by sarahh

Ahh ok--so the reason why it's over 8 is because of the other 5 possibilities?? That is:

HHH
TTT
THH
HTH
HHT

When each outcome is equally likely (which they are here), the probabilty is given by

$\displaystyle \frac{\text{Number of successful outcomes}}{\text{Number of possible outcomes}}$ .

In your problem, the number of successful outcomes = 3 and the number of possible outcomes = 8. So the probability is 3/8.