An international bank has branches in North America and Europe. From experience,

Question

An international bank has branches in North America and Europe.   From experience, 60% of its leveraged buyout (LBO) attempts in North American succeed while 40% of its LBO attempts in Europe succeed.  

a. If there are 10 LBO attempts in North America at this time, what is the probability that there will be at least 8 successful ones?

b. If there are 5 LBO attempts in North America and 5 LBO attempts in Europe, what is the probability that there will be more successes in Europe than in North America?

Explanation / Answer

a. Probability of successful LBOs in North America p = 0.6.

n = 10

X ~ Binom(10,0.6).

P(X >= 8) from tables = 0.1673.

b. X ~ Binom(5,0.6)

Y ~ Binom(5,0.4)

P(X = 0) = 0.01024 P(X > 0) = 0.92224

P(X = 1) = 0.0768 P(X > 1) = 0.66304

P(X = 2) = 0.2304 P(X > 2) = 0.31744

P(X = 3) = 0.3456 P(X > 3) = 0.08704

P(X = 4) = 0.2592 P(X > 4) = 0.01024

Probability that there will be more successes in Europe than in North America =

0.01024 * 0.92224 + 0.0768 * 0.66304 + 0.2304 * 0.31744 + 0.3456 * 0.08704 + 0.2592 * 0.01024

= 0.1662.

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