A county containing a large number of rural homes is thought...

A county containing a large number of rural homes is thought to have 60% of those homes insured against fire. Four rural homeowners are chosen at random from the entire population, and x are found to be insured against fire. (Round your final answers up to four decimal places.) (a) Find the probability distribution for x. Show your work when you calculate p(x = 0), p(x = 1), p(x = 2), p(x = 3) and p(x = 4). Then, copy the following table on a piece of paper and fill in the corresponding probability values. x 0 1 2 3 4 Sum p(x) (b) What is the probability that at least three of the four will be insured?

Transcript

00:01 Hey everyone according to the question we given that 60 % homes insured against fire and let xb denotes the number of home owners found to be insured against fire okay so now we let the probability that none of four is insured against fire okay so we have to find out in the question we have to find out the probability when none of the four is ensured against wire so we have to simply find out the probability of when x is equal to 0 so this is equals to 1 minus 0 .4 raised power 4 that is equal to 0 .4 raised power 4 we simplify this and we have 0 .256 okay now we have to calculate the probability that 1 of the force 4 is ensured against fire okay now we have to find out simply we have to find out the probability when x is equals to 1 so in this we use here the binomial distribution so we have to calculate this and this is equal to 4 multiply 0 .6 multiply 0 .4 raised about 3 okay in the large form we can write it as 0 .6 multiply by 1 minus 0 .6 multiply 1 minus 0 .6 that is i am writing on the sheet that is equal to 4 multiply 0 .6 multiply 0 .4 raised power 3 okay now in the step 3 of 8 we have to calculate the probability that 1 of the 4 is ensured against fire so this is equal to we simplify 0 .6 multiply 0 .4 rast to power 3 and we simplify this and we have 0 .1536 now we have to calculate the probability that 2 of the 4 is insured against fire means we have to find out when probability when x is equal to 2 so 4 c2 0 .6 raised to power 2 multiply 0 .4 to power 2 okay so we simplify this and we have 6 multiply 0 .6 raised to power 2 and multiply 0 .4 raised power 2 so we simplify this and we have 0 .3 4 5 6 okay now by step 5 of 8 we have to find out the probability that 3 of the 4 is insured again.

02:29 Against fire okay now simply we have calculate probability when x is equal to 3 this is 4 c3 0 .6 raised to 5 x x multiplied 0 .4 we simply define this and we have the answer 0 .3456 okay now last step of the question that is the probability when all are insured against fire all the home times are insured against fire so we have to calculate the probability when x is equal to 4 that is and 4c4 0 .6 raised to power 4 that is equal to 0 .196 so now in the step 7 of 8 we have to find out the probability distribution of x okay now we have to make the table of this probability distribution of x when x is equal to 0 what is the probability when x equal to 1 0 1 2 3 4 we have to find out the probability above okay simply we here put the values 0 .0 256 0 .1536 0 .3 .0 .3456.

03:33 0 .3456.

03:35 And for the x equal to 4, the probability is 0 .196...

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