Kate and Danny each have $10.
Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than $10 but less than $15?
Answer/Solution
15/32
Steps/Work
the probability of the coin landing tails up either 3 or 4 times = P(3t) + P(4t)
Binomial distribution formula: nCk p^k (1-p)^(n-k)
P(3t) = 5C3 (1/2)^3 (1/2)^2 = 10 (1/2)^5
P(4t) = 5C4 (1/2)^4 (1/2)^1 = 5 (1/2)^5
=> P(3t) + P(4t) = 15/32
Answer:D
Binomial distribution formula: nCk p^k (1-p)^(n-k)
P(3t) = 5C3 (1/2)^3 (1/2)^2 = 10 (1/2)^5
P(4t) = 5C4 (1/2)^4 (1/2)^1 = 5 (1/2)^5
=> P(3t) + P(4t) = 15/32
Answer:D