Provide an Appropriate Response in N Independent Trials, the Probability Of Only

question 130

Multiple Choice

Provide an appropriate response.
-The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes
Denoted by A, B, and C $\text { Let } \mathrm { P } ( \mathrm { A } ) = \mathrm { p } _ { 1 } , \mathrm { P } ( \mathrm { B } ) = \mathrm { p } _ { 2 } , \mathrm { P } ( \mathrm { C } ) = \mathrm { p } _ { 3 }$ . In n independent trials, the probability of $\mathrm { X } _ { 1 }$ outcomes of type A, $X 2$ outcomes of type B, and $X3$ outcomes of type C is given by $\frac { \mathrm { n } ! } { \left( \mathrm { x } _ { 1 } \right) ! \left( \mathrm { x } _ { 2 } \right) ! \left( \mathrm { x } _ { 3 } \right) ! } \cdot \mathrm { p } ^ { \mathrm { x } } 1 \cdot \mathrm { p } ^ { \mathrm { x } _ { 2 } } \cdot \mathrm { p } _ { 3 } ^ { \mathrm { x } _ { 3 } }$ A genetics experiment involves four mutually exclusive genotypes identified as A, B, C, and D, and they are all
Equally likely. If 10 offspring are tested, find the probability of getting exactly 2 A's,3 B's,3 C's, and 2 D's by
Expanding the above expression so that it applies to four types of outcomes instead of only three. Round your
Answer to five decimal places.

• A) 0.00601
• B) 0.04807
• C) 0.09613
• D) 0.02403

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Definitions:

Heroin

An opioid drug made from morphine, a natural substance taken from the seed pod of various opium poppy plants, known for its highly addictive properties.

Withdrawal Symptoms

Physical or psychological symptoms that follow the abrupt discontinuation or decrease in intake of a substance.

Endorphins

Neurotransmitters produced in the brain that act as natural painkillers and are also involved in feelings of pleasure or euphoria.

Opiates

A group of drugs derived from opium used for their analgesic, sedative, and narcotic effects.