A mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt. Th

Question

13 days ago

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e chance that the dart thrower hits the bullseye at least once in 6 attempts is:

1 answer:

lawyer [12.1K] · Answer 1 · 2026-03-28T05:22:12+03:00

Answer:

The likelihood of achieving the bullseye at least one time in 6 attempts is 0.469.

Step-by-step explanation:

It's stated that a mechanical dart thrower independently releases darts with a 10% probability of hitting the bullseye for each throw.

The chance of hitting the bullseye in a single throw, p = 0.10

The probability of failing to hit the bullseye on each throw, q = 1-p = 1-0.10 = 0.90

Let x represent the event of hitting the bullseye.

Our goal is to determine the probability of striking the bullseye at least once in 6 throws.

$P(x\geq 1)=1-P(x=0)$ .... (1)

According to the binomial formula

$P(x=r)=^nC_rp^rq^{n-r}$

where n refers to total attempts, r is the success count, p is the probability of success, and q denotes the failure probability.

The probability that the dart thrower fails to hit the bullseye in 6 attempts is

$P(x=0)=^6C_0(0.10)^0(0.90)^{6-0}$

$P(x=0)=0.531441$

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

$P(x\geq 1)=1-0.531441$

$P(x\geq 1)=0.468559$

$P(x\geq 1)\approx 0.469$

Thus, the probability of hitting the bullseye at least once across 6 attempts is 0.469.