Question

Olivia flips a two-sided counter and then spins a spinner with six equal-size sections labeled 1 through 6. One side of the counter is red. The other side is yellow. She performs this experiment 80 times. The relative frequency of tossing red and spinning a number greater than three was 2/5 . What is the difference between the number of expected outcomes and the number of actual outcomes?

Answer 1

12

Explanation:

A 2 - sided counter ; (red, yellow)

A spinner (1,2,3,4,5,6)

Number of trials = 80

P(red and number > 3) :

P(red) = 1/2 ;

P(number >3) : numbers greater Than 3 = (4, 5, 6)

Hence, P(number <3) = 3 /6 = 1/2

Theoretical probability = 1/2 *1/2 = 1/4

Expected number of outcomes :

1/4 * number of trials

1/4 * 80 = 20

Experimental outcome :

Relative frequency = number of outcomes / number of trials

Relative frequency = 2/5

Hence,

2/5 = number of outcomes / 80

Cross multiply :

160 = number of outcomes * 5

Number of outcomes = 160 /5 = 32

Actual outcomes = 32

Difference between actual and expected :

32 - 20 = 12