Amechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt. the chance that the dart thrower hits the bullseye at least once in 6 attempts is:

The probability of hitting the bullseye at least once in 6 attempts is 0.469.

Step-by-step explanation:

It is given that a mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt.

The probability of hitting bullseye in each attempt, p = 0.10

The probability of not hitting bullseye in each attempt, q = 1-p = 1-0.10 = 0.90

Let x be the event of  hitting the bullseye.

We need to find the probability of hitting the bullseye at least once in 6 attempts.

      .... (1)

According to binomial expression

where, n is total attempts, r is number of outcomes, p is probability of success and q is probability of failure.

The probability that the dart thrower not hits the bullseye in 6 attempts is

Substitute the value of P(x=0) in (1).

Therefore the probability of hitting the bullseye at least once in 6 attempts is 0.469.

100,000 miles

Step-by-step explanation:

Cost of Car A = $10,000

Cost of Car B = $11,000

Let the mile at which the cost are the same =x

Car A costs $0.12 per mile to maintain i.e. $0.12x for x miles

Car B costs $0.11 per mile to maintain i.e. $0.11x for x miles

Total Cost for Car A=10000+0.12x

Total Cost for Car B=11000+0.11x

If their costs are the same at x miles

10000+0.12x=11000+0.11x

0.12x-0.11x=11000-10000

0.01x=1000

x=1000/0.01=100,000

After 100,000 miles their total cost will be the same