Question

homework: unit 4 - mean, median and mode, and probability
question 34, 7.4.49
two dice are tossed. find the probability of getting the sum of the dice equal to 5. (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 5 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 \(6\times6 = 36\) since the outcomes of the first - die toss can combine with the outcomes of the second - die toss in multiple ways.

Step2: Find number of favorable outcomes

The pairs of numbers on the two dice that sum to 5 are \((1,4)\), \((2,3)\), \((3,2)\), \((4,1)\). 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:

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