Question

2 dies are tossed together.Find tge probability (i)that no.of each diesis eben(ii) sum on the 2 dies is 5

Answer 1

Hi there!
Here's the answer:


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¶ Total No. of outcomes when n dice are rolled = 6^n

¶ Probability of an Event = No. of Favourable Outcomes of that Event ÷ Total No. of Outcomes

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¶¶¶ SOLUTION :

Let S be sample space
n(S) - No. of total outcomes when 2 dice are rolled
n(S) = 6² = 36


•••• Let E1 be the Event that No. showed on both dice after rolling is even

There are 3 even No. possibilities for each die
•°• Total No. of possibilities = 2³ = 8
(Here 2 is considered as base due to fact that there are 2 dice)
or Count by considering cases as below

E1 = { (2,2) , (2,4) , (2,6) , (4,2) , (4,4) , (6,2) , (6,4) , (6,6) }


n(E1) is nothing but No. of possible cases in set E1
n(E1) = 8.

•••• Let E2 be the Event that Sum on the two dice is 5

E2 = { (1,4) , (2,3) , (3,2) , (4,1) }
n(E2) = 4


Now,

(i) Required probability

P(E1) = n(E1)/n(S) = 8/36 = 2/9

(ii) Required probability

P(E2) = n(E2)/n(S) = 4/36 = 1/9

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Hope it helps