SME
Grade 9 Science · Problem type
A sex-linked trait
Use this for “A carrier mother and a father with normal vision: what is the chance a son is color-blind?”
Diagram
1 of 4 boxes show the trait and 1 of 4 are carrier daughters.
A son gets his X from his mother, so one recessive allele is enough for him.
This is an example. Choose your own values to start a new problem.
m
Xᴮ alleles in the mother
example
f
Xᴮ alleles in the father
example
r
Boxes of 4 color-blind
worked out (not typed)
t
Boxes of 4 with normal vision
worked out (not typed)
k
Boxes of 4 carrier daughters
worked out (not typed)
s
Chance a son is color-blind
worked out (not typed) · %
Formulas
r
=
(2
−
m
)
×
(2
−
f
)
1 = (2 − 1) × (2 − 1)
t
=
4
−
r
3 = 4 − 1
k
=
f
×
(2
−
m
)
+
(1
−
f
)
×
m
1 = 1 × (2 − 1) + (1 − 1) × 1
s
=
50
×
(2
−
m
)
50 = 50 × (2 − 1)
Assumptions
•
Xᴮ is normal color vision and Xᵇ red–green color blindness; the Y chromosome carries no copy.
•
Sons get their only X from their mother, so one Xᵇ makes a son color-blind; males are never carriers.
•
A daughter needs Xᵇ from both parents to show the trait; with one she is a carrier.
Step-by-step
WE KNOW
m = 1, f = 1
FIND
boxes of 4 color-blind (r), boxes of 4 with normal vision (t), boxes of 4 carrier daughters (k), chance a son is color-blind (s)
Step 1 · Find boxes of 4 color-blind (r)
Use r = (2 − m) × (2 − f)
Each
Xᵇ
from
the
mother
makes
one
color-blind
son,
and
one
color-blind
daughter
too
when
the
father’
s
X
is
Xᵇ.
r
=
(2
−
1)
×
(2
−
1)
r
=
1
Step 2 · Find boxes of 4 with normal vision (t)
Use t = 4 − r
The other boxes have normal vision.
t
=
4
−
1
t
=
3
Step 3 · Find boxes of 4 carrier daughters (k)
Use k = f × (2 − m) + (1 − f) × m
A
carrier
daughter
has
one
Xᴮ
and
one
Xᵇ:
the
father’
s
X
paired
with
the
mother’
s
other
allele.
k
=
1
×
(2
−
1)
+
(1
−
1)
×
1
k
=
2
−
1
k
=
1
Step 4 · Find chance a son is color-blind (s)
Use s = 50 × (2 − m)
A
son
gets
one
of
his
mother’
s
two
X
at
random:
50%
for
each
Xᵇ
she
has.
s
=
50
×
(2
−
1)
s
=
50%
Check
Put the numbers back in. Both sides should match.
1 = (2 − 1) × (2 − 1) ✓
3 = 4 − 1 ✓
1 = 1 × (2 − 1) + (1 − 1) × 1 ✓
50 = 50 × (2 − 1) ✓
Topic check
See what you know: 5 questions on this topic
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