Probability |

**Probability Facts:**

**Probability is the likelihood that an event will occur from random chance****Probabilities are always between 0 and 1****Probabilities can be written as fractions, decimals or percentages****All possible events together must have a probability of 1****The probability that an event will not occur is 0****To find the probability of a particular event, we use this formula:**

Number of successful events(where a successful event is the result that you are looking ) | ||

Probability of an event | = | ——————————————— |

Total number of events |

**Whenever a coin is flipped, there is a 50% chance of getting heads & a 50% chance of getting tails.****The chance of inheriting one of two alleles from a parent is also 50%**

**Applying Probability to Mendel’s Peas:**

**During the late 1850’s, Gregor Mendel used the general rules of probability to explain the basic principles of heredity by breeding green peas in planned experiments****Different versions of genes are called alleles****For most genes, two alleles exist****If an organism has two different alleles for the same gene, the dominant allele will be expressed in the phenotype of the organism, while the recessive allele will not****Each parent will pass on one of its two alleles**

**Probability Laws:**

**The Law of Multiplication or Product Rule states that the chance of two or more independent events occurring together is the product of the probability of the events occurring separately**

Example: The chance of inheriting a specific allele from one parent & another allele from the other parent is 1/2 x 1/2 or 1/4**The following table shows the probability of the offspring genotypes whenever two heterozygous parents are crossed:**

Parents Rr x Rr | ||

Offpring RR | 1/2 x 1/2 = | 1/4 |

Offpring Rr | 1/2 x 1/2 = | 1/4 |

Offpring r r | 1/2 x 1/2 = | 1/4 |

**Complete the following table for crossing 2 Homozygous parents: **

Parents RR x rr | ||

Offpring Rr | |

**Click here for the correct answer**

**Example 1**

**Imagine we are rolling a fair dice. There are six equally likely outcomes: 1, 2, 3, 4, 5 and 6.**

- What is the probability of getting a five?

**In this case there is only one successful outcome or event, 5.**

Number of successful events | ||

Probability of a five | = | ——————————————— |

Total number of events | ||

1 | ||

Probability of a five | = | ———- |

6 |

- What is the probability of getting an even number?

In this case there are 3 successful outcomes, which are**2**,**4**and**6**.

Number of successful outcomes | ||

Probability of an even number | = | ———————————— |

Total number of outcomes | ||

3 | ||

Probability of an even number | = | ———- |

6 | ||

1 | ||

Probability of an even number | = | ———- |

2 |

**Therefore the probability of getting an even number when rolling a dice is 50% or 1/2.**

**Now apply these numbers to the dihybrid cross RrYy x RrYy****Probability of being R_ Y_ is 3/4 x 3/4 = 9/16****Probability of being R_ y_ is 3/4 x 1/4 = 3/16****Probability of being r_Y_ is 1/4 x 3/4 = 3/16****Probability of being r ryy is 1/4 x 1/4 = 1/16****This matches our 9:3:3:1 phenotypic ratio.**

**Example Problem:**

**Work a trihybrid cross of heterozygous parents — RrYyGg x ****RrYyGg**

**What is the probability of having a dominant gene for all three traits?****What is the probability of being recessive for all three traits?****What is the probability of being dominant for 2 and recessive for one?****What is the probability of being dominant for 1 and recessive for two?**

**Click here for the correct answers**

**The Law of Addition****is used when considering the probability of either of two mutually exclusive events****T****he individual probabilities of the 2 exclusive events are added**

Example:**The probability of selecting the three of clubs or any ace from the deck is the sum of the individual probabilities: P****robability of selecting a three of clubs = 1/52**

Probability of selecting any ace = 4/52

Total probability = 1/52 + 4/52 = 5/52