 # Two dice are thrown at the same time. `
Question:

Two dice are thrown at the same time. Find the probability of getting different numbers on both dice.

Solution:

It is given that two dice are thrown at the same time.

We have to find the probability of getting different numbers on both dice.

Total number of possible choices in rolling a dice = 6

Total number of possible choices in rolling two dice [Using multiplication rule] Probability of getting same number if two dice are thrown

$\mathrm{P}($ Same Number $)=\frac{6}{36}$

Probability of getting different number if two dice are thrown

$=1-\mathrm{P}($ Same Number $)$

$=1-\frac{6}{36}$

$=\frac{30}{36}$

$=\frac{5}{6}$

OR

It is given that a coin is tossed two times.

Therefore, sample space is given by,

{HH, HT, TH, TT}

Let E be the event of getting two heads. I.e., E = {HH}

Then, probability of getting atmost one head is given by

$P\left(E^{\prime}\right)=P(H T$ or $T H$ or $T T)=1-P(E)=1-P(H H)=1-\frac{1}{4}=\frac{3}{4}$