Respuesta :
Answer:
[tex]P(Pink) = \frac{1}{4}[/tex]
[tex]P(Both\ Black) = \frac{9}{16}[/tex]
[tex]Probability = \frac{3}{64}[/tex] --- Two pink and One black
Step-by-step explanation:
Represent the pink skin with P and the black skin with B.
Since black skin is dominant to pink skin, there will be more occurrence of B than P
The punnet square for the breeding of the two pigs is then represented as:
[tex]\begin{array}{cc} {B} & {B} \ \\ {B} & {P} \ \ \end{array}[/tex]
Solving (a): Probability of Pink
In the above square, there is only 1 occurrence of P out of a possible of 4.
So, the probability is:
[tex]P(Pink) = \frac{n(P)}{4}[/tex]
[tex]P(Pink) = \frac{1}{4}[/tex]
Solving (b): Probability that first and second are black
In the above square, there is only 3 occurrence of B out of a possible of 4.
[tex]P(Black) = \frac{n(B)}{4}[/tex]
[tex]P(Black) = \frac{3}{4}[/tex]
So, the probability that both are black is:
[tex]P(Both\ Black) = P(Black) * P(Black)[/tex]
[tex]P(Both\ Black) = \frac{3}{4} * \frac{3}{4}[/tex]
[tex]P(Both\ Black) = \frac{9}{16}[/tex]
Solving (c): Probability of two pink and 1 black
This is calculated as:
[tex]Probability = P(Pink) * P(Pink) * P(Black)[/tex]
[tex]Probability = \frac{1}{4} * \frac{1}{4} * \frac{3}{4}[/tex]
[tex]Probability = \frac{3}{64}[/tex]
A) The probability that their offspring will have pink skin is; ¹/₄
B) The probability that the first and second off- spring will have black skin is;
9/16 or 56.25%
C) The probability that two will be pink and one will be black If the pigs produce a total of three piglets is; ³/₆₄ or 4.6875%
Mendel's law of dominance
To answer this question, we need to first understand Mendel's law of dominance. This law states that in a heterozygote, one trait will conceal the presence of another trait for the same characteristic. This means that the dominant trait always conceal the recessive trait.
Now in this question, we are told that;
- black skin colour is dominant to Pink skin colour in pigs.
Let's denote the black color gene by ‘P’ and pink colour by ‘p’. Therefore, if cross is held between these two genes then according to mendel's law, the heterozygous pigs is specified as "Pp"
Now when the heterozygous pigs specified as "Pp" are crossed, we have;
Pp × Pp = PP, Pp, Pp, pp
where;
- PP and Pp denotes black pigs is denoted
- pp denotes pink pigs
(a) From the 4 cross possibilities above;
Probability that their offspring will have pink skin = ¹/₄
(b) From the 4 cross possibilities gotten earlier;
Probability that their offspring will have black skin = ³/₄
Thus;
Probability that the first and second off- spring will have black skin is;
³/₄ × ³/₄ = 9/16 or 56.25%
(c) We are told that the pigs produced a total of three piglet. Thus, the probability that two will be pink and one black will be black is;
P(2 pink and 1 black) = ¹/₄ × ¹/₄ × ³/₄ = ³/₆₄ or 4.6875%
Read more about Mendel's law of dominance at; https://brainly.com/question/14436268
