A box contains three coins which have the same look. However, two of them are fair and theother one is biased withP(H) = 0.3. A coin is randomly selected from the box and tossed 10 times.(a)[15 points] What is the probability of observing exactly 3 heads?

0.1673 (16.73%)

Step-by-step explanation:

The probability that a fair coin is chosen is 2/3 . if the fair coin is chosen the probability of getting 3 heads is determined by binomial distribution:

P(3 heads in 10 flips )=B(n=10,p=0.5,X=3) =0.1171

But if a coin that is not fair is chosen , then the probability of getting 3 heads also follows a binomial distribution but with p=0.3

P(3 heads)=B(n=10,p=0.3,X=3)=0.2668

Finally the probability is

P= 2/3*0.1171 + 1/3* 0.2678 = 0.1673 (16.73%)

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

company a

step-by-step explanation:

using the linear regression models , it is found that company a   pays about $14 more. but using the same regression (linear) company b pays about $10 more.

so company a pays more than b