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Answer:
The probability that these four will contain at least two more high-risk drivers than low-risk drivers is 0.0488.
Step-by-step explanation:
Denote the different kinds of drivers as follows:
L = low-risk drivers
M = moderate-risk drivers
H = high-risk drivers
The information provided is:
P (L) = 0.50
P (M) = 0.30
P (H) = 0.20
Now, it given that the insurance company writes four new policies for adults earning their first driver’s license.
The combination of 4 new drivers that satisfy the condition that there are at least two more high-risk drivers than low-risk drivers is:
S = {HHHH, HHHL, HHHM, HHMM}
Compute the probability of the combination {HHHH} as follows:
P (HHHH) = [P (H)]⁴
= [0.20]⁴
= 0.0016
Compute the probability of the combination {HHHL} as follows:
P (HHHL) = × [P (H)]³ × P (L)
= 4 × (0.20)³ × 0.50
= 0.016
Compute the probability of the combination {HHHM} as follows:
P (HHHL) = × [P (H)]³ × P (M)
= 4 × (0.20)³ × 0.30
= 0.0096
Compute the probability of the combination {HHMM} as follows:
P (HHMM) = × [P (H)]² × [P (M)]²
= 6 × (0.20)² × (0.30)²
= 0.0216
Then the probability that these four will contain at least two more high-risk drivers than low-risk drivers is:
P (at least two more H than L) = P (HHHH) + P (HHHL) + P (HHHM)
+ P (HHMM)
= 0.0016 + 0.016 + 0.0096 + 0.0216
= 0.0488
Thus, the probability that these four will contain at least two more high-risk drivers than low-risk drivers is 0.0488.
Start by distributing the exponent to each of the terms in . This will become
, and
. Now, the expression is:
.
We can now simplify the bottom to read: because when multiplying variables raised to an exponent, we add the exponents. The expression now looks like:
The 2/8 simplifies to 1/4:
Now, we have two u terms on the top and bottom. When dividing variables raised to an exponent, we subtract the exponents. However, since 3-5=-2, the term will be on the bottom to avoid the negative exponent. The final answer is:
Hope this makes sense!!