Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
In Toronto, Canada, there is a 90% chance of having a sunny day. What is the probability that there will be exactly 3 sunny days in the next 7 days?
Other
Community
NNikitesh
A
0.9
B
0.00255
C
0.0625
D
0.00125
Explanation:
This is a binomial probability problem where:
- n = 7 (number of trials/days)
- k = 3 (number of successes/sunny days)
- p = 0.9 (probability of success/sunny day)
- q = 1 - p = 0.1 (probability of failure/not sunny day)
The binomial probability formula is: P(k) = C(n,k) * p^k * q^(n-k) Where C(n,k) = n!/((n-k)!*k!)
Calculation: C(7,3) = 7!/(4!*3!) = (7×6×5)/(3×2×1) = 35 p^k = 0.9^3 = 0.729 q^(n-k) = 0.1^4 = 0.0001
P(3) = 35 × 0.729 × 0.0001 = 35 × 0.0000729 = 0.0025515 ≈ 0.00255
This matches the calculation provided in the text: P(3) = 7!/((7-3)!*3!) * 0.9³ * (1-0.9)⁷⁻³ = 0.00255
Comments
Loading comments...