Question

If a cat with short brown hair (llBb) is crossed with a cat with long black hair (Llbb), what is the likelihood that there will be offspring with long black hair AND short brown hair? A: 1/16 B: 3/4 C: 1/2 D: 1/4

Answer 1

Bb = brown hair phenotype

bb = black hair phenotype

we see that B = brown hair is the dominant gene while b = black hair is the recessive gene

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ll = short hair, this is a lowercase L

Ll = long hair

In this case, l = short hair is the recessive gene while L = long hair is the dominant gene.

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Check out the diagram below to see the dihybrid crosses for each of the hair color and hair length genotypes. From there, I show all of the genotypes possible for any offspring. Those genotypes are

• LlBb  = long brown hair (comes up 4 times)
• Llbb  = long black hair (comes up 4 times)
• llBb  = short brown hair (comes up 4 times)
• llbb  = short black hair (comes up 4 times)

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If we are talking about 1 offspring, then it is not possible for him/her to have both "long black hair AND short brown hair" as the instructions state. So let's consider two offspring instead.

The probability of having long black hair is 4/16 = 1/4 as there are 4 cases of Llbb out of 16 cases total. Similarly, the probability of getting llBb is 4/16 = 1/4 as well, for pretty much the same reasons.

The probability of having both events occur is (1/4)*(1/4) = 1/16

The multiplication of probabilities is valid because the two events are independent.

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Final Answer: A) 1/16