Help with detailed explanations please. thanks! variables lab_exercises 3 Random

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Help with detailed explanations please. thanks!

variables lab_exercises 3 Random Variables Lab Exercises: Problem 3 Next Problem professor is currently trying to get rid of a pesky magpio. The bird hassles the squirrels, makes a lot of noise early in the morning, ard is a general nuisance. Armed with a sling shot, the professor has three sling-shot peliots and thereforo has three chances tont me magpie. Because the magpie will not "sit stilr, the professor suggests there is a 0.65 probability of hitting the magpie on his first attempt with the sling-shot If the magpie is not hit on the first shot, the probability of thitting the magpie decreases by 0.05 for every shot thereafter A random vanable X is to count the number of shots the professor takes at the magpie. Complete the probability distribution af X below and use this to find the probability that at least two shots are taken at the magpie. Compute all probabilities to two decimals. (use two decimals in your answer) Preview My Answers Submit Answers

Explanation / Answer

At first hit success probability is 0.65 so failure is 1-0.65=0.35

To find P(X=2)=P(success at 2nd)

=p(success at 2nd|failure at 1st)*p(failure at first)

=0.60*0.35 [0.6 as probability decrease by 0.05 in 2nd draw]

=0.210

Similarly failure ar 2nd is

P(failure at 2nd|failure at 1st) *p(failure at 1st)

=0.4*0.35

=0.14

So P(X=3)=0.14*0.55=0.077

So more than 3 is that is p(x>3)=1-0.65-0.21-0.077=0.133

So p(x>=2)=p(x=2)+p(x>=3)=0.21+0.077+0.133=0.42

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