Mr David white promised his wife,Sabrina Bamba,a handsome amount of
$100,000 for preparing for him a very sumptuous meal.Mr David White
would not his promise.According to him,he made the promise jokingly
and that the wife would not be entitled to anything.Annoyed by the
behavoiurof her husband,Sabrina Bamba threatens to bring an action to
compel her husband to honour his promise.
  what are her chances of success?

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This question relates to consideration, try
en.wikipedia.org/wiki/Consideration for an introduction to this area
of contract.  In law there are often not simple right or wrong
answers, you need to cite cases both for and against the notion that
the wife's meal constituted valid consideration for the husband's
promise.

The are three issues.

First, a copurt would be very unlikely to settle a dispute of this
sort betwqeen a husband and wife (regardless of any legal merit)

Second, was there a meeting of the minds, if the husband did not
intend to contract, there may not be a contract. However, the wife can
claim relief based on detrimental reliance (she relied on the promise
to her detriment) or quasicontract (unjust enrichment)

The third is consideration.  Maybe it s a wife's job to cook her
husband a good meal, in which case, there would be no consideration.

Thw wife would lose.  No court would touch this.  they do not want to
be in the business of getting between marital problems.

The fundamentals of a valid contract are (1) compenancy of the Parties
to enter into Contract; (2) Lawful object; and the (3)lawful
consideration.  although not specified in the law, it is essential
that the object and consideration are commensurate to each other.  A
consideration of $ 100,000 for cooking a sumptuous meal would never be
a legally acceptable consideration.  Reasons are (1) the phrase
'sumptuous' is not defined and hence how could one decide whether or
not the meal was sumptuous; and/or (2) the constliest meal could be
available anywhere in world for a consideration at the fraction of the
offered amount.  Hence in the first instance the consideration itself
would be held void.

Secondly the contract consists of an Offer, and its acceptance.  The
so called promise made by David at best qualify for an offer and this
need to be accepted by his wife before contract comes into being. 
There is nothing to demonstrate that this pormise was ever accepted by
his wife.

Third David and his wife are related entities with conflict and/or
related interest.  Offer to pay this $ 100,000 could be interpreted as
transfer of assets by the husband to wife and provisions of other laws
like gift, tax evation etc. may also come onto surface for deciding
the issue.  And in all likely hood, the so called contract is Void and
hence not enforeceable.

Wife will not be able to enforce the contract, there being none.