Question

A Harris Interactive Survey for InterContinental Hotels and Resorts asked respondents, "When traveling internationally, do you generally venture out on your own to experience culture, or stick with your tour group and itineraries?" The survey found that 23% of the respondents stick with their tour group.

In a sample of 6 internationals travellers, what is the probability that 2 will stick with their tour group?

Answer 1

Answer:the probability that 2 will stick with their tour group is 0.21

Explanation:

The survey found that 23% of the respondents stick with their tour group. This means that the probability of success,

p is 23/100 = 0.23

Probability of failure, q = 1 - p = 1 - 0.23

q = 0.77

Number of international travellers sampled, n is 6

Assuming a binomial distribution for the responses, the formula for binomial distribution is

P(x = r) = nCr × q^(n-1) × p^r

To determine the probability that 2 will stick with their tour group, we would determine

P( x= r = 2). It becomes

6C2 × 0.77^(6-1) × 0.23^2

= 15 × 0.77^5 × 0.0529

= 0.21