Question

This problem Involves empirical probability. The table shows the breakdown of 87 thousand Single parents on active duty In the U S. military In a certain year. All numbers are In thousands and rounded to the nearest thousand. Use the data In the table to find the probability that a randomly selected single parent in the U S. military IS In the Army.

Army Navy Marine Corps Air force Total
Male 27 22 4 11 64
Female 11 7 1 4 23
Total 38 29 5 15 87

The probability that a randomly selected single parent in the U S military is In the Army is:_______

A certain lottery consists of selecting five different numbered balls from numbered 1 to 16 white balls and one from 1 to 12 gold Mega balls. A player wins the jackpot by matching all five numbers drawn from white balls​ (1 through 16​) and matching the number on the gold Mega Ball​ (1 through 12​). What is the probability of winning the​ jackpot?

The probability of winning the Jackpot is:______

Answer 1

1.) 38/87

2.) 1 / 56784

Explanation:

Given the data :

_____Army_Navy_ MarineCorps_ Air force_ Tot

Male__ 27___ 22____ 4________11 ______64

Female 11____ 7 _____1 _______ 4 ______23

Total _ 38___ 29____ 5_______ 15 ______87

The probability that a randomly selected single parent in the U S military is In the Army is:_______

P = number of required outcome/ Total possible outcomes

P(single parent) :

Number of required outcomes = (number of single parents in the army = 38000

Total number of single parents in the military = 87000

P(single parent in army) = 38000 / 87000 = 38/87

B) To Win Jackpot:

16C5

Using the combination formula:

n! / (n-r)!r!

Using calculator :

16C5 = 4368

Winning number set = 1

Probability of winning number set = 1 / 4368

Probability of picking a correct (1) gold mega ball

Number of gold mega balls = 13

= 1/13

1/4368 * 1/ 13 = 1 / 56784