# Probability Problems

• Oct 15th 2009, 04:21 PM
loutja35
Probability Problems
Boods Types: The probability that a person in the United States has type AB+ blood is 3%. Five unrelated people in the United States are selected at random.
a.) Find the probability that all five have AB+ blood.
b.) Find the probability that none of the five has type AB+ blood.
c.) Find the probability that at least one of the five has type AB+ blood.

Guessing: A multiple-choice quiz has three questions, each with five answer choices. Only one of the choices is correct. You have no idea what the answer is to any question and have to guess each answer.
a.) Find the prob. of answering the first question correctly.
c.) Fine the prob. of answering all three questions correctly.
c.) Find the prob. of answering the first two questions correctly.
d.) Find the prob. of answering none of the questions correctly.
e.) Find the prob. of answering at least one of the questions correctly.
• Oct 15th 2009, 07:51 PM
Soroban
Hello, loutja35!

Quote:

Blood Types:
The probability that a person in the United States has type AB+ blood is 3%.
Five unrelated people in the United States are selected at random.

We have: .$\displaystyle \begin{Bmatrix}P(\text{AB+}) \:=\:0.03 \\ P(\text{Not}) \:=\:0.97 \end{Bmatrix}$

Quote:

a) Find the probability that all five have AB+ blood.
$\displaystyle P(\text{5 AB+}) \:=\:(0.03)^5 \:=\:0.0000000243$

Quote:

b) Find the probability that none of the five has type AB+ blood.
$\displaystyle P(\text{5 Not}) \:=\:(0.97)^5 \:=\: 0.8587340267$

Quote:

c) Find the probability that at least one of the five has type AB+ blood.
This is the exact opposite of part (b).

$\displaystyle P(\text{at least one AB+}) \;=\; 1 - 0.85873402578 \;=\;0.1412650743$