Question

For the following example, state whether the trials are independent or dependent.

9-year-old Lucy gets to pick from the candy bag, filled with colored jelly beans, every time she helps around the house. She has been picking (and eating!) candy for 5 days in a row and each time she has picked a different color jelly bean.

(Note: The candy bag was only filled one time and no more candy has been added since then.)

Answer 1

An independent trial is when the chance of an event happenning remains the same every time the trial happens.

Lets take for eg that the candy bag has only 5 different coloured jelly beans say red, blue green, yellow and black. Probability that she picks any one of these colours on the first day = 1/5. Now suppose she picked a red on the first day and we do not refill the candy bag with a red candy. Now when she goes for another candy the next day, is the probability of picking a blue, green, yellow or black = 1/5 as on the first day? No, the probability has now become 1/4, and hence the probability has changed. Then such an event is therefore a dependent event.

In the given example, as Lucy keeps on taking out a candy from the candy bag, and with no replacement happenning, the probability of her picking the next candy piece willkeep on changing, and hence these are dependent events.