Question

A pair of dice is thrown three times.If getting a double is considered as a success find the probability of getting two successes

Answer 1

Answer:

5 / 72

I hope this helps you.

Step-by-step explanation:

When a pair of dice are thrown, there are 36 possible outcomes: 6 possibilities for each die, so 6 × 6 = 36 in total.

There are 6 ways to get a double though:  double 1, double 2, ...., double 6.

So the probability of getting a double is 6 / 36 = 1/6.

That is, for each throw of the pair of dice:

p = P(success) = 1/6

Now with 3 throws (presuming we are interested in exactly 2 successes, not at least 2 successes)...

P(exactly 2 successes)

= p²(1-p) × ( # ways 2 successes can be distributed over 3 throws )

= $\displaystyle\binom32p^2(1-p)$

= 3 p² (1-p)

= 3 × 5 / 6³

= 5 / 72