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content/public/unsorted/q0413/q0413.md

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+---
+title: Eye color, Part I
+topic: Distributions of random variables
+author: Larry Gu
+source: original
+template_version: 1.4
+attribution: openintro-stats
+partialCredit: true
+singleVariant: false
+showCorrectAnswer: false
+outcomes:
+- 4.1.1.5
+- 4.1.1.6
+- 4.1.1.9
+- 4.1.1.10
+difficulty:
+- undefined
+randomization:
+- undefined
+taxonomy:
+- undefined
+span:
+- undefined
+length:
+- undefined
+tags:
+- L. G.
+assets: null
+part1:
+  type: number-input
+  pl-customizations:
+    atol: 0
+    rtol: 0
+    weight: 1
+    allow-blank: true
+    label: $$p =$$
+part2:
+  type: number-input
+  pl-customizations:
+    atol: 0.01
+    rtol: 1.0e-07
+    weight: 1
+    allow-blank: true
+    label: $$\mu =$$
+part3:
+  type: number-input
+  pl-customizations:
+    atol: 0.01
+    rtol: 1.0e-07
+    weight: 1
+    allow-blank: true
+    label: $$\sigma =$$
+myst:
+  substitutions:
+    params_c1: 0.375
+    params_c2: 0.5
+    params_c3: 0.125
+    params_p1: 0.125
+    params_p: 0.5
+    params_mu: 2.0
+    params_sig: 1.41
+---
+# {{ params.vars.title }}
+A husband and wife both have brown eyes but carry genes that make it possible for their children to have brown eyes (probability {{params_c1}}), blue eyes ({{params_c2}}), or green eyes ({{params_c3}}).
+
+## Part 1
+
+What is the probability the first blue-eyed child they have is their third child? Assume that the eye colors of the children are independent of each other. Enter exact number.
+
+## Part 2
+
+On average, how many children would such a pair of parents have before having a blue-eyed child? Round to 2 decimal places.
+
+## Part 3
+
+For the previous part, what is the standard deviation of the number of children they would expect to have until the first blue-eyed child? Round to 2 decimal places.
+
+## Attribution
+
+Problem is from the [OpenIntro Statistics](https://openintro.org/book/os/) textbook, licensed under the [CC-BY 4.0 license](https://creativecommons.org/licenses/by/4.0/).<br>![Image representing the Creative Commons 4.0 BY license.](https://raw.githubusercontent.com/firasm/bits/master/by.png)