Question

1. In a community of 214 monkeys exposed to harmful chemicals, 83 have respiratory problems, 58 have liver problems, and 28 have both. Consider the following event: E: Having respiratory or liver problems. Find P (E).
A. 0.53
b. 0.55
c. 0.30
d. 0.35
E. None of the above

2. In the first round of a tennis tournament all players must face each other exactly once. If there are 15 players in the first round, how many matches do they have to take place?
A. 225
b. 210
c. 105
d. 125
E. 90

3. A supervisor will evaluate 10 employees randomly, out of a total of 35, in how many ways can he do it?
A. 6.6 x 1014
b. 183,579,396
c. 155,234,111
d. 123,901,987
E. None of the above

Answer 1

Q1) The probability here is computed using the law of additivity:
P(respiratory or liver problems)

= P( respiratory problems) + P( liver problems) - P(both)

= (58 + 83 - 28) / 214

= 0.53

Therefore 0.53 is the required probability here.

Q2) As all players are to face each other in the first round, therefore the total number of matches for 15 players is computed as the number of ways to select 2 players for a match from 15 players

Therefore c) 105 is the required number of matches that will take place here.

Q3) Total ways to select 10 employees from 35 is computed here as:

Therefore B) is the required number of ways here.