What is the probability that a fair die never comes up an even number when it is

Tobias Ali

Tobias Ali

Answered question

2021-10-19

What is the probability that a fair die never comes up an even number when it is rolled six times?

Answer & Explanation

saiyansruleA

saiyansruleA

Skilled2021-10-20Added 110 answers

a

DEFINITIONS 
Product law The number of ways that two events can occur in succession is then if one event can happen in m different ways AND a second event can happen in n different ways. mn
b
SOLUTION 
Six different outcomes are possible when rolling a die: 1, 2, 3, 4, and 6.
First roll: 6 ways 
Second roll: 6 ways 
Third roll: 6 ways 
Fourth roll: 6 ways 
Fifth roll: 6 ways 
Sixth roll: 6 ways 
Use the product rule: 
666666=66=46656 
Even number of outcomes for each roll
The possible outcomes of a die are 1, 2, 3, 4, and 6. Three of the results are equal: 2, 4, 6
First roll: 3 ways 
Second roll: 3 ways 
Third roll: 3 ways 
Fourth roll: 3 ways 
Fifth roll: 3 ways 
Sixth roll: 3 ways 
Use the product rule: 
333333=36=729 
Step 3 
Probability 
Every roll yields an even result in 729 of the 46656 cases.
The probability is calculated by dividing the number of likely outcomes by the total number of outcomes.
P(6heads)=offav or aboutcomesofpossiboutcomes=72946656=164=0.015625

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?