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avets where thare ave only two poybu outcome wh o Posib e outcoma B. Show the fo

ID: 3367009 • Letter: A

Question

avets where thare ave only two poybu outcome wh o Posib e outcoma B. Show the formula and calculate how to determine the probability of getting 2 threes if you roll a ten-sided die 5 times. C. Show the formula and calculate how to determine the probability of getting all threes if you roll a ten-sided die 5 times. D. What is the expected number of threes if you roll a ten-sided die 5 times? (4) 5. A. What is a geometric distribution? B. Show the formula and calculate how to determine the probability of getting two threes before you get another number if you roll a ten-sided die 5 times. C. What is the espected number of threes you roll before you roll another number? D. When is real life might you use a geometric distribution to calculate probability?

Explanation / Answer

5. A.

The geometric distribution represents the number of failures before one success in a series of independent trials, where each trial results in either success or failure, and the probability of success in any individual trial is constant. For example, if you toss a coin, the geometric distribution models the number of tails observed before getting a heads.

B.

Probability of getting a three in ten-sided die = 1/10 = 0.1

Probability of getting a number other than three in ten-sided die, 9/10 = 0.9

Let the probability of success, p = 0.9 and probability of failure, 1-p = 0.1

By Geometric distribution, the probability of getting two threes before you get another number = p(1-p)2

= 0.9 * 0.12 = 0.009

C.

Bu Geometric distribution, expected number of threes you roll before you roll another number = (1 - p) / p = 0.1 / 0.9 = 1/9 = 0.1111

D.

A real life example of a geomtric distribution is to determine the probability of number of tails observed before getting a heads in a toss of a fair coin.