Question

Two dice are thrown simultaneously and getting a number less than 3 on a die is termed as a success. obtain the probability distribution of the number of successes?

Answer 1

Answer:

1/3

Explanation:

Total no of outcomes=12(as there are two dices thrown)

No less than 3=1,2

p(of getting a number less than 3)=4/12

Answer 2

Two dices are thrown simultaneously and the probability of the number of the successes, i.e. less than 3 = $\frac{5}{9}$

Numbers that are below 3 = 1,2

• Probability of the outcome,i.e. number of successes for each dice, P(S) = $\frac{2}{6}= \frac{1}{3}$

• Probability of failure, P(F) = $1-\frac{1}{3}=\frac{2}{3}$.

The probability distribution of success

=1st success*2nd failure+1st failure*2nd success+1st success*2nd success

=P(S)P(F)+P(F)P(S)+P(S)P(S)

=$\frac{1}{3}*\frac{2}{3}+\frac{2}{3}*\frac{1}{3}+\frac{1}{3}*\frac{1}{3} = \frac{5}{9}$.