Question

A spinner has a pointer which can land on one of the three regions labelled 1, 2, and 3 respectively. compute the expected value for the number on which the pointer lands if the probabilities for the three regions are 12,16, and 13 respectively.

Answer 1

To calculate the expected value of a spinner with regions labelled 1, 2, and 3 with given probabilities, multiply each outcome by its probability and sum the results. The expected value in this case is approximately 1.83.

Step-by-step explanation:

To compute the expected value for the number on which the spinner lands with probabilities 1/2, 1/6, and 1/3 for regions 1, 2, and 3 respectively, we use the formula for the expected value (E) in probability, which is:

E = (x1 × p1) + (x2 × p2) + (x3 × p3)

Where x1, x2, and x3 are the possible outcomes, and p1, p2, and p3 are the probabilities of each respective outcome occurring. In this case, the possible outcomes are landing on regions labelled 1, 2, and 3, with their corresponding probabilities being 1/2, 1/6, and 1/3.

So, the expected value is calculated as follows:

E = (1 × 1/2) + (2 × 1/6) + (3 × 1/3)

E = 0.5 + 0.3333 + 1

E = 1.8333

The expected value of the spinner is approximately 1.83.