Probability Binomial With Parameters

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Sub: Statistics Topic: Probability

Probability Binomial with Parameters

Question:

Among Orthodox Jews, families are expected to be large. Among Ashkenazim, a segment of the

Jewish population, Tay-Sachs disease is [TSD] a relatively common disorder. TSD is an inherited

autosomal recessive disorder, i.e., both parents must be carriers in order that a child inherits the

disease. Suppose 2 such Ashkenazim parent-carriers have 12 children. What is the probability that:

[1] No children will have TSD?

[2] At least 1 child will be born with TSD?

[3] No more than 2 children will have TSD?

To use the binomial applet, click onto Distribution Calculators”. A graph will appear, and on the left

side there will be a column labeled “Distributions/ Parameters”. Click on the down arrow on the right

hand side of that column; then scroll the slide up to “Binomial Distribution”, then click onto it. Set the

number of trials, N, success probability, p, in the windows provided to answer the above questions.

Move the mouse to the appropriate columns and the values will appear on the graph. Press the “Print

Screen” key on your PC to obtain a copy of your results.

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Sub: Statistics Topic: Probability

Solutions:

In this case we can find the required Probabilities using the Binomial distribution with parameters

n = 3 and p = 3/4

n r n r

I. P[ No children will have TSD ] = p q

r

3

= 0.25 0 0.75 3 0

0

= 0.753

= 0.421875

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*The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for

submitting the same in lieu of their academic submissions for grades.

Sub: Statistics Topic: Probability

II. P[at least 1 child will be born with TSD] = P[ X = 1,2, 3]

= 1 – P[X = 0]

= 1 - 0.421875 (Taken from the previous section)

= 0.578125

III. P[no more than 2 children will have TSD] = P[ X = 0, 1, 2]

= P[X = 0] + P[X = 1] + P[X = 2]

3 3 3

= 0.25 0 0.75 3 0 + 0.2510.75 3 1 + 0.25 2 0.75 3 2

0 1 2

= 0.421875+ 0.421875 + 0.140625

= 0.98425

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*The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not fo

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