Question

An urn contains 9 pink and 7 black balls. Four 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 balls drawn from the urn are pink? Round your answer to three decimal places.

Answer 1

gotcha! ok here we go

Answer 2

thank you

Answer 3

lets think about the probability of picking a single pink ball

if there are 9 pink balls and 7 black balls this means there are 16 balls in total

to work out the probability of picking a single pink ball with one trial we can work out the probability like this:
\[P(\text{ball is pink}) = \frac{\text{number of pink balls}}{\text{total number of balls}}\]

this means if we picked out 1 ball, the probability of it being pink would be
\[\frac{9}{16}\]

does this make sense?

Answer 4

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Answer 5

now if we pick more than one ball we have to consider it as more than one event

each time we repeat the event we have to multiply the probabilities

the probabilities are all the same (9/16) because we replace the balls after picking them

so we have

\[\frac{9}{16} \times \frac{9}{16} \times \frac{9}{16} \times \frac{9}{16} \]

Answer 6

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