Respuesta :
Answer:
[tex]\left ( \frac{1}{216} \right )[/tex]
Step-by-step explanation:
Total number of outcomes when a dice is rolled = 6^2 = 36
As the sum of the two numbers showing is greater than or equal to 10,
possible outcomes are [tex]\left \{ (4,6),(6,4),(5,6),(6,5),(6,6),(5,5) \right \}[/tex].
Independent events are the events in which occurrence of one event remains unaffected with the occurrence of other events.
Its given that if the sum of the two numbers showing is greater than or equal to 10, you win.
Probabilty = Number of favourable outcomes/Total number of outcomes.
Here,
Number of favourable outcomes = 6
Probability that you win the first time = [tex]\frac{6}{36}=\frac{1}{6}[/tex]
Probability that you win the second time = [tex]\frac{6}{36}=\frac{1}{6}[/tex]
Probability that you win the third time = [tex]\frac{6}{36}=\frac{1}{6}[/tex]
Therefore, the probability that you win the first three times you play = [tex]\left ( \frac{1}{6} \right )\times \left ( \frac{1}{6} \right )\times \left ( \frac{1}{6} \right )=\left ( \frac{1}{216} \right )[/tex]
