Question

Matt and his wife have 20 good friends, twelve of them are male and eight of them are female. They decide to have a diner party but can invite only eight guests. They decide to invite their guests by drawing their names from a hat. What is the probability that a) There will be an equal number of males and females at the dinner party? b) Mandie will be among those invited? c) There will be only one female guest? d) They will have only male guests? e) There will be at least one female guest?

Answer 1

a) Probability that there will be an equal number of males and females at the party is computed here as:
= Number of ways to select 4 males from 12 males * Number of ways to select 4 females from 8 females / Total ways to select 8 names from 20 names

Therefore 0.2751 is the required probability here.

b) Probability that  Mandie will be among those invited is computed here as:
= Number of ways to select remaining 7 from remaining 19 guests/ Total ways to select 8 guests from 20 guests

therefore 0.4000 is the required probability here.

c) Probability that there will be only one female guest

= Number of ways to select 7 males from 12 males * Number of ways to select 1 female from 8 females / Total ways to select 8 guests from 20 guests

Therefore 0.0503 is the required probability here.

d) Probability of only male guests

Therefore 0.0039 is the required probability here.

e) Probability of at least one female guest

= 1 - Probability of only male gues

= 1 - 0.0039

= 0.9961

Therefore 0.9961 is the required probability here.