Question

34. Two different dice are thrown simultaneously. Find the probability of getting:
(i) a number greater than 3 on each dice
(ii) an odd number on both dice.
home time Find the probability of getting:​

Answer 1

$$$\frac{1}{16}$$

Solution:

Two dice are thrown.

Let A be the getting a number greater than 3 on each.

Let B be the getting odd number on both dice.

The image of the sample space is attached below.

Number of sample space N(s) = 36

Getting a number greater than 3 on each

= (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)

N(A) = 9

Probability of getting 3 on each dice:

$$$P(A)=\frac{N(A)}{N(S)}$$

$$$=\frac{9}{36}$$

$$$P(A)=\frac{1}{4}$$

Getting odd an number on both dice

= (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3 5), (5, 1), (5, 3), (5, 5)

N(B) = 9

Probability of getting an odd number on both dice:

$$$P(B)=\frac{N(B)}{N(S)}$$

$$$=\frac{9}{36}$$

$$$P(B)=\frac{1}{4}$$

Probability of getting a number greater than 3 on each dice and an odd number on both dice:

$$$P(A \cap B)=P(A)\times P(B)$$

$$$=\frac{1}{4}\times\frac{1}{4}$$

$$$=\frac{1}{16}$$

Hence the probability of getting a number greater than 3 on each dice and an odd number on both dice is $$\frac{1}{16}$$ .

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