MATH: statistic/ probalitity - need help problem with #9-25 (a, a-c) - related q

Question

MATH: statistic/ probalitity
- need help problem with #9-25 (a, a-c)
- related questions
- please explain/show steps/answer to the question

ty that something will not happen Sometimes it is easier to figure out the probabili than the probability that it will. When finding the probability that something will happen, you are looking at the complement. The complement is the set of all outcomes in the sample space that are not included in the outcomes of the event, 9.25. Will not Show two ways to solve the problem below then decide which way you prefer and explain why 1Crystal is spinning the spinner at right and claims she has a good chance of having the spinner land on red at least once in three tries. What is the probability that the spinner will land on red at least once in three tries? Red Blue Yellow

Explanation / Answer

Question 3 : part (i)

number of colors = 3

P( Getting red at single trials) = 1/3

n = number of trials =3

X : number of red in three trials

Since each trial is independent of each other.

X ~ Bin( n =3 , p=1/3)

P ( At least one red in three trials) = P(X >=1)

which can be obtained in two ways

A) by using complement

P(X>=1) = 1 - P(X=0)

= 1- ( 3C0 * (1/3)0 * (2/3)3)

= 1- 0.2962 = 0.7038

P ( At least one red in three trials) = 0.7038

B) P(X> =1) = P(X=1) + P(X=2) + P(X=3)

= ( 3C1 * (1/3)1* (2/3)2)+ ( 3C2 * (1/3)2 * (2/3)1) + ( 3C3 * (1/3)3 * (2/3)0)

= ( 3 *(1/3) *(2/3)2 ) +  ( 3 *(1/3)2 *(2/3) ) +  ( 3 *(1/3)3 *(2/3)0 )

=0.4444 + 0.2222 + 0.0370

= 0.7038

The first way easier than second way i.e by using complement ( beacuse we have to find probability at one point.)

Part ii)

n = total number of households = 1060

a) Number of household earned over $ 85000 = 230

P( Earning over $ 85000) = 230 /1060 = 0.2169

b) Number household having no pets = 222

P( Having no pets ) = 222/1060 = 0.2094

c) P( having a pet)

By using complement

P(Having a pet ) = 1 - P(having no pet)

P(Having a pet) = 1 - 0.2094 = 0.7906

Household income Number with premarily dogs Number with premarily cats Number with premarily birds Number with premarily horses Number with no pets Total Under $20000 64 63 69 3 70 269 $20000 to $34999 66 59 7 3 41 176 $35000 to $54999 77 66 8 4 38 193 $55000 to $84999 82 68 7 4 31 192 $85000 and over $85000 97 77 9 5 42 230 Total 386 333 100 19 222 1060

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