148k views
5 votes
According to police sources, a car with protection system will be recovered 50% of the time. find the probability that exactly 3 out of 7 cars will be recovered:

A. 0.2734
B. 0.1641
C. 0.0547
D. 0.0078

User Lorenz
by
8.6k points

1 Answer

4 votes

Final answer:

The probability that exactly 3 out of 7 cars with a protection system will be recovered, given a 50% chance of recovery per car, is 0.2734 (option A).

Step-by-step explanation:

The question is asking for the probability that exactly 3 out of 7 cars with a protection system will be recovered, given that a car with a protection system will be recovered 50% of the time.

This is a typical binomial probability problem, where the number of trials is 7 (the number of cars), the number of successes sought is 3 (the cars recovered), and the probability of success on a single trial is 0.5 (50% chance of recovery).

To calculate the probability, we use the binomial probability formula:

P(X = k) = C(n, k) × p^k × (1-p)^(n-k),

where:

  • P(X = k) is the probability of k successes in n trials,
  • C(n, k) is the number of combinations of n items taken k at a time, often written as n choose k,
  • p is the probability of success on a single trial,
  • n is the total number of trials,
  • k is the number of successful trials.

Plugging in the values we have:

P(X = 3) = C(7, 3) × 0.5^3 × (1-0.5)^(7-3),

Calculating this we get:

P(X = 3) = 35 × 0.125 × 0.0625 = 0.2734375,

So, the probability that exactly 3 out of 7 cars will be recovered is 0.2734, which corresponds to option A.

User Willthefirst
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories