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HW 4.4 Score: 13.7/23 11/15 answered X Question 11 < Score on last try: 0 of 3 pts. See Details for more. > Next question Try a similar question You can retry this question below Suppose that 26% of students who take a class pass. You repeteadly ask students until you find one who passed. Find the probability that: Round to three decimals. a. The first person who passed is the 10 th or 15 th person you ask : re b. The first person who passed is somewhere between (inclusive) the 10 th and 15 th people : c. The first person who passed is either before the 10 th person or after the 15 th : Submit Question Jump to Answer tor

Answer 1

Solution .. let X: The number persons /students until who take a class find one person you class pass. - 26% P: proportion of students who takes class pass = 0.26 .:. Probabiling from this above information, the random variable 2 follows geometric dishi bution coith dishibution with parameter p'-0.26 function of x is given by P[X=8] - [PC1-p3 ; 2=0.1,2, mass 8 oape ; otherwise O and cumulative probabiliny function for geometric distribution is 0 K<0 1 Fx(x) = P[x<a] ; x 7,0 (1-P) 2+1 son who is the 10th or 15th -> That is here we have to ca) Find probabiling that the first person passed person you ask ? find probability P[ X=10 or X=15] - ? P[X10 o X-15) - P[x210] + P[X= 15] P [x=40 o X-15) - (0.26) [1-0,26]° + (0.26)(1-0.26]" 15 > 7

=> Plx=10 on X: 1s] = 0.26 (0.797 +60.74)" ] - 0.26 (0.060166 2713) 0.0156432305 P[x = 10 or x=15 ] = 0.0156 rounded to 4 decimal P[x=10 m Xz15] - 0.016 3 decimal places first cb) The “person who passed is some where between (inclusive) loth and isth person ? That is, we have to find Ρ[ιο 10 < x $15] P[105 x315) P[X=15] - P[X <10] P[ X5.15] P[xs9 by using CDF of ₂ 157 1- (1-0.26) [1-(1-0,2 1.0.26) ? 9+'] 16 10 1 - (0.74) – 1 + 0.74) (0.7%) 0 (0.74) 16 こ 0.0415439 22 P[10 X 415] = 0.041 rounded to 3 decimal person (c) The first person who passed either before 10th Or after the 15th person n ? is we have to Pla - 10 or x > 15) - That have to find

- PlXc10 Oy x>15] - P(x<10] # P[*> is] P[*39] + 1- P(x315) by using cof of [-1 (1-0203") * -- [9.610.2016] 10 16 = 1-(0.74) +1-1 + (0.74) -1-0.79)'0 +(0.749" - | - 0.0492399 + 0.0080855 = 0.9588456 rounded to 3 decimal or x > 15] = 0.959 ed is who that, is 0.016 > P1X<10 Resur! ca) The probability the first person the 10th or 15th person (b) The probability that the first person somewhere between (inclusive) the 10th fisth person first person probabiliny after 15th either before 10th person person passed passed who is SOD is 0.041 i's who that, the passed (C) The is an 0.959