This is due today (10 points) urpi and manco are playing a game where they flip a fair coin four times and try to predict the outcomes. using the sample space of possible outcomes listed below, answer each of the following questions. 1) what is p(a), the probability that the second flip is heads? 2) what is p(b), the probability that the fourth flip is heads? 3) what is p(c), the probability that the second flips is heads and the fourth flip is heads? 4) are events a and b independent?

Remark

There are 16 results of throwing a coin 4 times.

Answer 4 first.

These are independent events. No matter what the first result or the second or the third result is outcome can only be 1/2 for any given throw. One event does not influence any other.

One

What this means is that it does not matter what else might be true as long as the second event is heads. So you count THTT and as both being true. If you use your table, I believe there are 8 results where heads is in the second position.

Two

The last position will also contain heats 8 times. Just count them up. Some of them will be duplicated from your first answer. It does not matter. For example, will appear in both lists.

Three

For Heads in the second AND the last position you should get 4. They are THHH THTH HHTH

Answers

P(one) = 8/16. You get 8 answers out of 16 to get a heads in position 2.

P(Two) = 8/16. You get 8 answers out of 16 to get a heads in position 4

P(Three) = 4/16. You get 4 answers out of 16 to get a heads in positions 2 and 4

answer:

1. 0.04

2. 0.15

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