Question

A fair die is tossed 5 times. Let " alt="\dfrac{m}{n}" align="absmiddle" class="latex-formula"> be the probability that at least two consecutive tosses have the same number, where m and n are relatively prime positive integers. Find m.

Answer 1

Answer:

m = 1

Step-by-step explanation:

We can suppose that the number we are looking for is for example 5.

(we can do so because the probability is the same for each number - it'sna fair dice)

For the first toss the probability we have 5 is 1/6 (we have 6 numbers on the dice and number 5 is just one of the possible 6 outcomes).

For the second toss the probability we have 5 is again 1/6.

For the rest of 3 tosses we don'tcare what number we will get( we have our two consecutive 5s), so all of the outcomes for the rest of 3 tosses are good for us (probability is 6/6 = 1)

Threfore, the probability to get two consecutive 5s is 1/6 * 1/6 * 1 * 1 * 1 = 1/36.

We can see that m = 1.