An urn contains 7 pink and 8 green balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball
is returned to the urn. What is the probability that all 6 balls drawn from the urn are pink? Round your answer to three decimal places.

Question

UpStudy AI · Accepted Answer

Let $$ P(\text{pink}) $$ be the probability of drawing a pink ball in one draw. Since the urn contains 7 pink and 8 green balls, the total number of balls is

$$
7 + 8 = 15.
$$

Thus, the probability of drawing a pink ball is

$$
P(\text{pink}) = \frac{7}{15}.
$$

Since each ball is replaced after the draw, the draws are independent. Therefore, the probability of drawing 6 pink balls in a row is

$$
\left( \frac{7}{15} \right)^6.
$$

Expanding, we have

$$
\left( \frac{7}{15} \right)^6 = \frac{7^6}{15^6}.
$$

Calculating the exponents:

$$
7^6 = 117649 \quad \text{and} \quad 15^6 = 11390625.
$$

Thus, the probability is

$$
\frac{117649}{11390625} \approx 0.010337.
$$

Rounded to three decimal places, the probability is

$$
0.010.
$$
The probability of drawing 6 pink balls in a row is approximately 0.010.

An urn contains 7 pink and 8 green balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball
is returned to the urn. What is the probability that all 6 balls drawn from the urn are pink? Round your answer to three decimal places.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Probability Questions

An urn contains 7 pink and 8 green balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 6 balls drawn from the urn are pink? Round your answer to three decimal places.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Probability Questions

An urn contains 7 pink and 8 green balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball
is returned to the urn. What is the probability that all 6 balls drawn from the urn are pink? Round your answer to three decimal places.