An Olympic archer misses the bull's-eye 15% of the time. Assume each shot is independent of the

An Olympic archer misses the bull's-eye 15% of the time....

An Olympic archer misses the bull's-eye 15% of the time. Assume each shot is independent of the others. If she shoots 9 arrows, what is the probability of each of the results described in parts a through f below? a) Her first miss comes on the eighth arrow. The probability is 0.0481. b) She misses the bull's-eye at least once. The probability is 0.7684. c) Her first miss comes on the second or third arrow. The probability is 0.2359. d) She misses the bull's-eye exactly 3 times. The probability is 0.1069. e) She misses the bull's-eye at least 3 times. The probability is .

Transcript

00:01 We have that the probability that that person will miss the bozzi is 0 .15, which is the same as saying that will not miss here, equals to 1 minus the probability of missing, which is 0 .85.

00:21 This is just so we know.

00:23 So in item a, what is the probability that in this case her first missed will come in the error number eight.

00:35 So this means that the first seven, she was okay.

00:38 So she got right all this first seven.

00:42 So we have like a, for the first seven, we have that she got right.

00:46 She did not miss, but then in the last one, she missed that one.

00:51 So this is how we do.

00:52 For the first seven, we are considering the probability of not missing.

00:56 And in the last one, the probability of missing.

00:59 So this is the answer.

01:02 Now for item b, we want what is the probability that she will miss at least once.

01:09 So if you say that x is the number of here, the number of shots that she miss, so let me.

01:23 We want to say this being at least one, which means that this is better to compute as one minus the complement.

01:31 So she will not miss any.

01:33 So this is the same as not missing.

01:36 1 minus not missing any.

01:39 And if she does not miss any, this means that all the 9 she got to write.

01:45 So that's why they have 085 at power 9 to express this.

01:49 So this is 1 minus 0 .2316.

01:54 So the final answer is 076 .84.

02:00 For item c here, we want to compute what is the probability that her first miss will be on the 6.

02:07 Second or third.

02:09 So let's say the first, let's consider that was in the second.

02:12 So this means that in the first one she got right, but in the second she got wrong...

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