Question

Which of the following experiments could be used to simulate an event in which the probability of success, P(success) is 1/3, and the number of successes out of 10 events is desired?

A. Use a spinner that is divided into 4 equal parts. Choose 1 color for a success; the other 3 colors will represent unsuccessful. Spin the spinner 10 times, once for each event.

B. Roll a die. Let 5 and 6 represent a success and the other values indicate unsuccessful. Roll the die 10 times, once for each event.

C. Count out 50 yellow beads and 50 pink beads. Randomly select 10 of these beads. Let a yellow bead represent a success and a pink bead represent unsuccessful.

D. Use a random number table with digits 1 and 2 representing a success and the remaining digits representing unsuccessful. Choose 10 digits, one for each event.

Answer 1

Option B has P(success) is 1/3.

Explanation :

in a dice we have number 1,2,3,4,5,6

chance of occuring 5 is 1/6 and chance of occuring 6 is also 1/6

so, here 5 & 6 represent success - so, 1/6 + 1/6 = 1/3

so, probability for single event will be 1/3.

Now, if die is rolled 10 times, then getting success in all the successive events will be

(1/3)^10

in Other options A, C and D - 1/3 probability is not possible.