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Answer:
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.