Question

• 1. Roger won a prize to go on a discounted tennis tournament for himself and 9 others.
  a) Upon posting on his social media page, people started expressing interest in joining him for the tournament. If from past experience, the probability that a random respondent is male is 0.65 and that it is female is 0.35, what is the probability that he gets at least 2 females in his first 10 responses?
  b) He has a total of 45 people (25 males and 20 female) interested to accompany him. If he picks randomly from this list, what is the probability that the tournament will have at least 1 other male?

Answer 1

Solution:

a) The number of female responses out of 10 responses is modelled here as:
X ~ Bin(n = 10, p = 0.35)

The probability now is computed as:

P(X ≥ 2) = 1-[ P(X = 0) + P(X = 1 )]
= 1-[¹⁰C₀ * 0.35⁰* 0.65¹⁰ + ¹⁰C₁ * 0.35¹ * 0.65⁹]
= 1-[0.0135 + 0.0725]
= 0.9140

Therefore 0.9140 is the required probability here.

b) Probability that he will have 1 other male is computed here as:

= Total males / Total responses = 25/45 = 0.556

Therefore 0.556 is the required probability here.