Spring 20188 You hit a Dart Board 5 times. The probability that you hit the Cent

Question

Spring 20188 You hit a Dart Board 5 times. The probability that you hit the Center and get a "Strike" is 0.2 Find the Probability that you get 4 strikes or more. 5Pt You invite 100 friends to your party. The probability that a friend will wear a red tie is 0.1 Use Normal Approximation of Binomial Probability Distribution to find the following probabilities: 1. Probability that 4 friends or less will be wearing a red tie. 2. Probability that 19 friends or more will be wearing a red tie. 1, = 2, = Ans: Prob: 4 or less wear red ties Ans: Prob: 19 o e wear red ties- 10 Pt Page 3 of 6

Explanation / Answer

You hit a dartboard n=5 times

p= prob to hit the ceter for strike = 0.2

We have to find the prob of x=4 or more strikes

i.e. P(x=4) + P(x=5)

So we have to use Binomial theorm here since we have the probability of success p = 0.2 is given and so the ptrob of failure q=1-p=0.8

So., using the equation of bimomial distribution

P(X=x) = nCx * p^x * q^(n-x)

P(Exact 4 hits) =P(X=4) = 5C4 * 0.2^4 * 0.8^1 = 0.0064 same way

P(Exact 5 hits) =P(X=5) = 5C5 * 0.2^5 * 0.8^0 = 0.00032

so. Ans= P(X>=4) = P(X=4)+P(X=5) =0.0064+0.00032 = 0.00672

Due to time constraint & the Chegg policy of answering 1 question at a time I won't be able to answer the next question. If you want the answer for the next question as well pls post it seperately. Hope you understand.

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!

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