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Phoenix [80]
3 years ago
9

You play a game that involves rolling a die. You can roll as many times as you want, but if you roll a six your score is zero an

d your turn is over. You attempt to devise a good strategy by simulating several plays to see what might happen. On what roll do you expect to get a six for the first time?
Mathematics
1 answer:
anyanavicka [17]3 years ago
5 0

Answer:

6

Step-by-step explanation:

P(6) = ⅙

Expected no. of trials for first 6:

1 ÷ (1/6) = 6

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Suppose approximately 75% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introvert
Setler [38]

Answer:

P(x \ge 5) = 1.000 ---- At least 5 from marketing departments are extroverts

P(x=15) = 0.013 ---- All from marketing departments are extroverts

P(x = 0) = 0.002 ---------- None from computer programmers are introverts

Step-by-step explanation:

See comment for complete question

The question is an illustration of binomial probability where

P(x) = ^nC_x * p^x * (1 - p)^{n-x}

(a):\ P(x \ge 5)

n = 15 --- marketing personnel

p = 75\% --- proportion that are extroverts

Using the complement rule, we have:

P(x \ge 5) = 1 - P(x < 5)

So, we have:

P(x < 5) =P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

P(x = 0) = ^{15}C_{0} * (75\%)^0 * (1 - 75\%)^{15 - 0} = 1 * 1 * (0.25)^{15} = 9.31 * 10^{-10}

P(x = 1) = ^{15}C_{1} * (75\%)^1 * (1 - 75\%)^{15 - 1} = 15* (0.75)^1 * (0.25)^{14} = 4.19 * 10^{-8}

P(x = 2) = ^{15}C_{2} * (75\%)^2 * (1 - 75\%)^{15 - 2} = 105* (0.75)^2 * (0.25)^{13} = 8.80 * 10^{-7}

P(x = 3) = ^{15}C_{3} * (75\%)^3 * (1 - 75\%)^{15 - 3} = 455* (0.75)^2 * (0.25)^{12} = 0.0000153

P(x = 4) = ^{15}C_{4} * (75\%)^4 * (1 - 75\%)^{15 - 4} = 1365 * (0.75)^4 * (0.25)^{11} = 0.000103

So, we have:

P(x < 5) = (9.31 * 10^{-10}) + (4.19 * 10^{-8}) + (8.80 * 10^{-7}) + 0.0000153 + 0.000103

P(x < 5) = 0.00011922283

Recall that:

P(x \ge 5) = 1 - P(x < 5)

P(x \ge 5) = 1 - 0.00011922283

P(x \ge 5) = 0.9998

P(x \ge 5) = 1.000 --- approximated

(b)\ P(x = 15)

n = 15 --- marketing personnel

p = 75\% --- proportion that are extroverts

So, we have:

P(x) = ^nC_x * p^x * (1 - p)^{n-x}

P(x=15) = ^{15}C_{15} * 0.75^{15} * (1 - 0.75)^{15-15}

P(x=15) = 1 * 0.75^{15} * (0.25)^{0

P(x=15) = 0.013

(c)\ P(x = 0)

n=5 ---------- computer programmers

p = 70\% --- proportion that are introverts

So, we have:

P(x) = ^nC_x * p^x * (1 - p)^{n-x}

P(x = 0) = ^{5}C_0 * (70\%)^0 * (1 - 70\%)^{5-0}

P(x = 0) = 1 * 1 * (0.30)^5

P(x = 0) = 0.002

3 0
2 years ago
Write and solve an equation to find your final score. Use x to represent your final score.
attashe74 [19]
Let your final bowling score be x. It is 14 pins less than your friends final score. Your friends final bowling score is 105. Then x is 14 pins less than 105.
1 way: This means that 105 is greater than x by 14. Mathematically,
105-x=14,
-x=14-105,
-x=-91,
x=91.
2 way: When you add 14 to x, you'll get 105.
x+14=105,
x=105-14,
x=91.
Answer: Your final score is 91.
8 0
2 years ago
Write an equation <br> Eight times the sum of m and 7 is 21
guajiro [1.7K]

Answer:

the equation would be 8(m+7)=21

6 0
2 years ago
Read 2 more answers
4x-35=9x<br><br>please help me i really need help
zhenek [66]
4x-35=9x
     -4x
-35=5x
divide by 5
x= -7
        
5 0
3 years ago
Read 2 more answers
Alan found the value of the expression (15 - 6)2 to be 189. Is he right?
tatuchka [14]
Answer would be C

Because I always use the rule of :
B - Brackets
I - indices
D - division
M - multiplication
A - addition
S - subtraction
3 0
3 years ago
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