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Forgive me English is not my first language so this is confusing?

Suppose you toss a coin 4 times. a. What is the probability that you will get exactly 3 heads? b. Explain what P*(not 3 heads) means

*P meaning Probability

Can anyone explain how I would solve this word problem? Thank you!!

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2 Answers

Hint: What is the probability that you will get exactly $0$ heads? What is the probability that you will get exactly one head? If it helps, there are $2^4$ possibilities for the sequence of four flips. Try writing them all out and see if you can spot a pattern.

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(a) There are four different outcomes that give you exactly $3$ heads: HTTT, THTT, TTHT, and TTTH. The probability of getting exactly $3$ heads is the probability of getting one of these four outcomes, so it is

$$\frac4{\text{number of possible outcomes}};$$

what is the total number of possible outcomes?

(b) You’re tossing four coins, so if you don’t get $3$ heads, what are the possible numbers of heads that you could get? $P(\text{not }3\text{ heads})$ is the probability of getting one of these other numbers of heads.

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Thank you! The total number of possible outcomes would be 16, so it would be 4/16 or 1/4? –  Miki Dec 13 '12 at 2:48
@Miki: That’s exactly right. –  Brian M. Scott Dec 13 '12 at 2:49
Thank you very much, I really appreciate it!! (: –  Miki Dec 13 '12 at 2:50
@Miki: You’re very welcome. –  Brian M. Scott Dec 13 '12 at 3:15
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