Question

Order the following events based on their theoretical probabilities, from highest probability to lowest. I. flipping a coin that lands heads up II. rolling a 5 using a number cube numbered 1 to 6 III. selecting a card with an odd number from a bag containing cards numbered 2-8

Answer 1

I. flipping a coin that lands heads up.

III. selecting a card with an odd number from a bag containing cards numbered 2-8.

II. rolling a 5 using a number cube numbered 1 to 6.

Explanation:

I. flipping a coin that lands heads up.

It has the highest probability as there has to be 1 outcome(heads or tails) in two choices. The probability is 1/2 or 0.5.

II. rolling a 5 using a number cube numbered 1 to 6.

There is a probability of 1/6 as 5 appears one time in 6 choices. So, 1/6 or 0.167. This has lowest probability.

III. selecting a card with an odd number from a bag containing cards numbered 2-8.

The odd numbers are 3,5,7 means there are 3 outcomes from 7 choices giving a probability of 3/7 or 0.428.

Now comparing all probabilities, we get 0.5 > 0.428 > 0.167

Or first option > third option > second option.

Answer 2

I. flipping a coin

III. selecting an odd-numbered card

II. rolling a 5

Explanation:

I. there are 2 outcomes from a coin flip, 1 of which is heads. The probability of a flipped coin landing heads up is 1/2.

II. Of the 6 faces of the number cube, 1 is a 5. The probability of rolling a 5 is 1/6.

III. Of the 7 cards in the bag, 3 are odd-numbered. The probability of selecting an odd-numbered card is 3/7.

1/2 > 3/7 > 1/6, so the ordering you want is I, III, II.