Punnett Squares and Binomials

= 0. 25R 2 + 05 . RW + 0.
25W
2
(red) (pink) (white)
Q: What does this model tell use about the probability of each event, and how is this
model consistent with the Punnett square?
A: This model implies that the probability of a red snapdragon offspring will be
⎛ 1
⎜
⎞ ⎝ 4⎠ ⎟ ⎛ 1
(25%), a pink offspring will be ⎜
⎞ ⎝ 2⎠ ⎟ ⎛ 1
(50%), and a white offspring will be ⎜ ⎞ ⎝ 4⎠ ⎟ (25%).
This is consistent with the area model because 25% of the area is red (RR), 50% of the
area is pink (RW), and 25% of the area is white (WW).
Closure/Extension:
Q: This is an amazing that pattern because it can be shown algebraically and
geometrically. Now that you have learned the pattern of a squared binomial, can anyone
think of this pattern of coefficients 1 : 2 : 1 in another part of mathematics?
A: Pascal’s triangle. Notice the coefficients when you perform various powers to
the same binomial. The pattern of coefficients represents Pascal’s triangle. Pascal’s
triangle is a pattern formed by adding two adjacent numbers and writing the solution
below the two numbers.
( a + b)
0
= 1
( a + b)
1 = 1 1
( a + b)
( a + b)
( a + b)
2
3
4
= 1 2 1
= 1 3 3 1
= 1 4 6 4 1
… = ……
Q: Using Pascal’s triangle, determine the coefficients of a binomial that is raised
to the 5 th power? 6 th power?
A: 5 th power = 1 5 10 10 5 1
6 th power = 1 6 15 20 15 6 1