A die is thrown twice. Find the probability that a number less than 4 is rolled at least once.

tamolam8 2022-09-11 Answered
A die is thrown twice. Find the probability that a number less than 4 is rolled at least once.
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Answers (1)

Medwsa1c
Answered 2022-09-12 Author has 17 answers
There are six possible outcomes in a single roll of a die: the number 1 or 2 or 3 or 4 or 5 or 6.
Only in three out of six cases will the event be favorable, i.e. a number less than 4 will come up: 1 or 2 or 3.
Therefore, the probability that a number less than 4 will come up when a die is rolled is: 3/6=1/2=0.5
The probability of an unfavorable event (a number less than 4 will never fall out) is: 0.5*0.5=0.25. Then the probability of a favorable event is: 1-0.25=0.75
or
Because the die is thrown twice, then the probability of events can be as follows: B - a favorable event (a number less than 4), H - an unfavorable event (a number greater than 4)
BH
BB
HB
HH
As you can see, the number of favorable events occurs in three out of four cases (BH, BB, HB), and the number of unfavorable events is one (HH - a number less than 4 will not fall out even once).
Then, the probability that at least once a number less than 4 fell out will be: 3/4=0.75=75%
Answer: The probability of rolling a number less than 4 at least once when rolling the die twice is 0.75

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