Sarthaks Test
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A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?

(i) that the sum of the two numbers that turn up is 8?

(ii) of obtaining a total of 6?

(iii) of obtaining a total of 10?

(iv) of obtaining the same number on both dice?

(v) of obtaining a total more than 9?

(vi) that the sum of the two numbers appearing on the top of the dice is 13?

(vii) that the sum of the numbers appearing on the top of the dice is less than or equal to 12?

1 Answer

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Total no. of possible outcomes when 2 dice are thrown = 6×6 = 36 which are

{ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) }

(i) E ⟶ event of getting sum that turn up is 8

No. of possible outcomes = 36

No. of favourable outcomes = 5 {(2, 6) (3, 5) (4, 4) (5, 3) (6, 2)}

P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes) = 5/36

(ii) Let E ⟶ event of obtaining a total of 6

No. of favourable outcomes = 5

{(1, 5) (2, 4) (3, 3) (4, 2) (5, 1)}

P(E) = 5/36

(iii) Let E ⟶ event of obtaining a total of 10.

No. of favourable outcomes = 3 {(4, 6) (5, 5) (6, 4)}

P(E) = 3/36 = 1/12

(iv) Let E ⟶ event of obtaining the same no. on both dice

No. of favourable outcomes = 6 {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}

P(E) = 3/36=1/12

(v) E ⟶ event of obtaining a total more than 9

No. of favourable outcomes = 6 {(4, 6) (5, 5) (6, 4) (5, 6) (6, 5) (6, 6)}

P(E) = 6/36 = 1/6

(vi) The maximum sum is 12 (6 on 1st + 6 on 2nd)

So, getting a sum of no’s appearing on the top of the two dice as 13 is an impossible event.

∴ Probability is 0

(vii) Since, the sum of the no’s appearing on top of 2 dice is always less than or equal to 12, it is a sure event.

Probability of sure event is 1.

So, the required probability is 1.

by (10 points)
The 4th part is incorrect as the possible outcomes should be 6

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