Question

unit 4 - statistics. two dice are tossed. find the probability of getting the sum of the dice equal to 9. (hint: draw a tree - diagram of the possibilities of two tosses of a die, and then find the sum of the numbers on each branch.) the probability of getting a sum of 9 is (type a whole number or a simplified fraction.)

Explanation:

Step1: Find total number of outcomes

When two dice are tossed, each die has 6 possible outcomes. So the total number of outcomes is \(6\times6 = 36\) according to the multiplication - principle.

Step2: Find number of favorable outcomes

The pairs of numbers on the two dice that sum to 9 are \((3,6)\), \((4,5)\), \((5,4)\), \((6,3)\). So there are 4 favorable outcomes.

Step3: Calculate probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P = \frac{4}{36}=\frac{1}{9}\).

Answer:

\(\frac{1}{9}\)