Question

In: Statistics and Probability

2. A child has a collection of 28 dyed eggs. There are 10 pink eggs, 8...

2. A child has a collection of 28 dyed eggs. There are 10 pink eggs, 8 green eggs, 6 yellow eggs, and 4 blue eggs. Suppose the child selects 6 eggs at random without replacement from this collection.

a) Find the probability the 6 eggs contain exactly 3 pink eggs.

b) Find the probability the 6 eggs contain 2 pink eggs, 1 green egg, 2 yellow eggs, and 1 blue egg.

c) Find the probability the 6 eggs contain exactly 2 green eggs and exactly 2 blue eggs.

d) Find the probability that half of the 6 eggs are pink and the other half are green.

e) Find the probability that none of the 6 eggs are pink and none of the 6 eggs are green.

Expert Solution

2.

a) probability the 6 eggs contain exactly 3 pink eggs

= Number of ways of selecting 3 pink eggs from 10 pink eggs and 3 non-pink eggs from 18 non-pink eggs / Number of ways of selecting 6 eggs from 28 eggs

b)probability the 6 eggs contain 2 pink eggs, 1 green egg, 2 yellow eggs, and 1 blue egg

= Number of ways of selecting 2 pink eggs from 10 pink eggs x Number of ways of selecting 1 green egg from 8 green eggs x number of ways of selecting 2 yellow eggs from 6 yellow eggs x number of ways of selecting 1 blue egg from 4 blue eggs / Number of ways of selecting 6 eggs from 28 eggs

c) Probability the 6 eggs contain exactly 2 green eggs and exactly 2 blue eggs

= Number of ways of selecting 2 green egg from 8 green eggs x number of ways of selecting 2 blue egg from 4 blue eggs x Number of ways of selecting 2 non blue and non-green eggs from 16 non-blue and non-green eggs / Number of ways of selecting 6 eggs from 28 eggs

d) Probability that half of the 6 eggs are pink and the other half are green

= Number of ways of selecting 3 pink eggs from 10 pink eggs and 3 green eggs from 8 green eggs / Number of ways of selecting 6 eggs from 28 eggs

e) Probability that none of the 6 eggs are pink and none of the 6 eggs are green =

= Number of ways of selecting 6 non-pink and non-green eggs from 10 non-pink and non-green eggs / Number of ways of selecting 6 eggs from 28 eggs

orchestra answered 1 year ago

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