The Binomial Distribution Applies Only to Cases Involving Two Types $$A , x _ { 2 }$$

question 63

Multiple Choice

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. Let P A = p1, P B = p2, P C = p3. In n independent trials, the probability of x1 outcomes of type $$A , x _ { 2 }$$ outcomes of type B, and x3 outcomes of type C is given by $$\frac { \mathrm { n } ! } { \left( \mathrm { x } _ { 1 } \right) ! \left( \mathrm { x } _ { 2 } \right) ! \left( \mathrm { x } _ { 3 } \right) ! } \cdot \mathrm { p } _ { 1 } \mathrm { x } _ { 1 } \cdot \mathrm { p } _ { 2 } ^ { \mathrm { x } _ { 2 } } \cdot \mathrm { p } _ { 3 } ^ { \mathrm { x } _ { 3 } }$$ A genetics experiment involves four mutually exclusive genotypes identified as A, B, C, and D, and they are all equally likely. If 13 offspring are tested, find the probability of getting exactly 2 A's,4 B's,2 C's, and 5 D's by expanding the above expression so that it applies to four types of outcomes instead of only three.

• A)0.96656
• B)0.03222
• C)0.00805
• D)0.00201

---

Definitions:

Escalation of Commitment

A phenomenon where individuals or organizations continue to invest in a decision despite facing negative outcomes or feedback, often due to a desire to justify prior investments.

Masculine Cultures

Cultures that value competitiveness, assertiveness, material success, and achievements associated with traditional male roles.

Assertive Decisions

Choices made confidently and firmly, demonstrating a clear stance without being aggressive, ensuring one's rights and needs are communicated effectively.

Knowledge Work

Refers to tasks that involve handling or using information, often requiring analytic skills, creativity, and intellectual effort.