Chapter 10.8, Problem 23STP

To determine

To find: The probability that the spinner lands on 2 and 5 respectively after it’s spun twice.

Answer to Problem 23STP

The correct answer is Option (A) $\frac{1}{64}$ .

Explanation of Solution

Given: A spinner is attached to a circular board which has 8 equal sectors marked 1 to 8. The spinner has equal chances of landing on any one of the 8 sectors.

Concepts Used: Consider an event that has m possible outcomes. If the same event is carried out n number of times then the total number of possible outcomes will be $m^n$ .

The probability of any event is the ratio of the number of favorable outcomes to the total number of possible outcomes.

Calculation: If the spinner is spun once it can land on any one of the 8 sectors so total number of possible outcomes is 8. Hence, if the spinner is spun twice total number of possible outcomes will be equal to $8^2=64$ .

Let E be the event that the spinner first lands on 2 and then on 5 after it’s spun twice.

Since there is only one possibility, i.e.- the event will occur if and only if the spinner lands first on 2 after the first spin and then on 5 after the second spin, thus total number of favorable outcomes = 1

Therefore the required probability is-

  $P(E)=\frac{1}{64}$

Thus, the correct answer is Option (A) $\frac{1}{64}$